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Question
x^{2}-2x-3=0
Solve the quadratic equation
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Solve by factoring
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Solve using the quadratic formula
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Solve by completing the square
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Solve using the PQ formula
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x_{1}=-1,x_{2}=3
Evaluate
x^{2}-2x-3=0
Factor the expression
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Evaluate
x^{2}-2x-3
Rewrite the expression
x^{2}+\left(1-3\right)x-3
Calculate
x^{2}+x-3x-3
Rewrite the expression
x\times x+x-3x-3
\text{Factor out }x\text{ from the expression}
x\left(x+1\right)-3x-3
\text{Factor out }-3\text{ from the expression}
x\left(x+1\right)-3\left(x+1\right)
\text{Factor out }x+1\text{ from the expression}
\left(x-3\right)\left(x+1\right)
\left(x-3\right)\left(x+1\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-3=0\\&x+1=0\end{align}
\text{Solve the equation for }x
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Evaluate
x-3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
\begin{align}&x=3\\&x+1=0\end{align}
\text{Solve the equation for }x
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Evaluate
x+1=0
Move the constant to the right-hand side and change its sign
x=0-1
Removing 0 doesn't change the value,so remove it from the expression
x=-1
\begin{align}&x=3\\&x=-1\end{align}
Solution
x_{1}=-1,x_{2}=3
x_{1}=-1,x_{2}=3
Evaluate
x^{2}-2x-3=0
\text{Substitute a=}1\text{,b=}-2\text{ and c=}-3\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{2\pm \sqrt{\left(-2\right)^{2}-4\left(-3\right)}}{2}
Simplify the expression
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Evaluate
\left(-2\right)^{2}-4\left(-3\right)
Multiply the numbers
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Evaluate
4\left(-3\right)
Multiplying or dividing an odd number of negative terms equals a negative
-4\times 3
Multiply the numbers
-12
\left(-2\right)^{2}-\left(-12\right)
Rewrite the expression
2^{2}-\left(-12\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
2^{2}+12
Evaluate the power
4+12
Add the numbers
16
x=\frac{2\pm \sqrt{16}}{2}
Simplify the radical expression
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Evaluate
\sqrt{16}
\text{Write the number in exponential form with the base of }4
\sqrt{4^{2}}
\text{Reduce the index of the radical and exponent with }2
4
x=\frac{2\pm 4}{2}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{2+4}{2}\\&x=\frac{2-4}{2}\end{align}
Simplify the expression
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Evaluate
x=\frac{2+4}{2}
Simplify
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Evaluate
\frac{2+4}{2}
Add the numbers
\frac{6}{2}
Reduce the numbers
\frac{3}{1}
Calculate
3
x=3
\begin{align}&x=3\\&x=\frac{2-4}{2}\end{align}
Simplify the expression
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Evaluate
x=\frac{2-4}{2}
Simplify
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Evaluate
\frac{2-4}{2}
Subtract the numbers
\frac{-2}{2}
Reduce the numbers
\frac{-1}{1}
Calculate
-1
x=-1
\begin{align}&x=3\\&x=-1\end{align}
Solution
x_{1}=-1,x_{2}=3
x_{1}=-1,x_{2}=3
Evaluate
x^{2}-2x-3=0
Add or subtract both sides
x^{2}-2x=3
Add the same value to both sides
x^{2}-2x+1=3+1
Simplify the expression
\left(x-1\right)^{2}=4
Take the root of both sides of the equation and remember to use both positive and negative roots
x-1=\pm \sqrt{4}
Simplify the expression
x-1=\pm 2
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x-1=2\\&x-1=-2\end{align}
Solve the equation
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Evaluate
x-1=2
Move the constant to the right-hand side and change its sign
x=2+1
Add the numbers
x=3
\begin{align}&x=3\\&x-1=-2\end{align}
Solve the equation
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Evaluate
x-1=-2
Move the constant to the right-hand side and change its sign
x=-2+1
Add the numbers
x=-1
\begin{align}&x=3\\&x=-1\end{align}
Solution
x_{1}=-1,x_{2}=3
x_{1}=-1,x_{2}=3
Evaluate
x^{2}-2x-3=0
Solve using the PQ formula
x=\frac{2}{2}\pm \sqrt{\left(\frac{-2}{2}\right)^{2}-\left(-3\right)}
Simplify the expression
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Evaluate
\left(\frac{-2}{2}\right)^{2}-\left(-3\right)
Divide the terms
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Evaluate
\frac{-2}{2}
Reduce the numbers
\frac{-1}{1}
Calculate
-1
\left(-1\right)^{2}-\left(-3\right)
Evaluate the power
1-\left(-3\right)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+3
Add the numbers
4
x=\frac{2}{2}\pm \sqrt{4}
Simplify the expression
More Steps
Evaluate
\sqrt{4}
\text{Write the number in exponential form with the base of }2
\sqrt{2^{2}}
\text{Reduce the index of the radical and exponent with }2
2
x=\frac{2}{2}\pm 2
Divide the terms
x=1\pm 2
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=1+2\\&x=1-2\end{align}
Evaluate
\begin{align}&x=3\\&x=1-2\end{align}
Evaluate
\begin{align}&x=3\\&x=-1\end{align}
Solution
x_{1}=-1,x_{2}=3
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