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Question
2x^{2}+12=44
Solve the quadratic equation
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Solve using square roots
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Solve by factoring
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Solve using the quadratic formula
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Solve using the PQ formula
More methods
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x_{1}=-4,x_{2}=4
Evaluate
2x^{2}+12=44
Add or subtract both sides
2x^{2}=32
Divide both sides
\frac{2x^{2}}{2}=\frac{32}{2}
Divide the numbers
x^{2}=16
Take the root of both sides of the equation and remember to use both positive and negative roots
x=\pm \sqrt{16}
Simplify the expression
x=\pm 4
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=4\\&x=-4\end{align}
Solution
x_{1}=-4,x_{2}=4
x_{1}=-4,x_{2}=4
Evaluate
2x^{2}+12=44
Move the expression to the left side
2x^{2}-32=0
\text{Use }a^2-b^2=(a-b)(a+b)\text{ to factor the expression}
2\left(x-4\right)\left(x+4\right)=0
Divide the terms
\left(x-4\right)\left(x+4\right)=0
When the product of factors equals 0,at least one factor is 0
\begin{align}&x-4=0\\&x+4=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x-4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
\begin{align}&x=4\\&x+4=0\end{align}
\text{Solve the equation for }x
More Steps
Evaluate
x+4=0
Move the constant to the right-hand side and change its sign
x=0-4
Removing 0 doesn't change the value,so remove it from the expression
x=-4
\begin{align}&x=4\\&x=-4\end{align}
Solution
x_{1}=-4,x_{2}=4
x_{1}=-4,x_{2}=4
Evaluate
2x^{2}+12=44
Move the expression to the left side
2x^{2}-32=0
\text{Substitute a=}2\text{,b=}0\text{ and c=}-32\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{0\pm \sqrt{0^{2}-4\times 2\left(-32\right)}}{2\times 2}
Simplify the expression
x=\frac{0\pm \sqrt{0^{2}-4\times 2\left(-32\right)}}{4}
Simplify the expression
More Steps
Evaluate
0^{2}-4\times 2\left(-32\right)
Calculate
0-4\times 2\left(-32\right)
Multiply
More Steps
Multiply the terms
4\times 2\left(-32\right)
Rewrite the expression
-4\times 2\times 32
Multiply the terms
-256
0-\left(-256\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
0+256
Removing 0 doesn't change the value,so remove it from the expression
256
x=\frac{0\pm \sqrt{256}}{4}
Simplify the radical expression
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Evaluate
\sqrt{256}
\text{Write the number in exponential form with the base of }16
\sqrt{16^{2}}
\text{Reduce the index of the radical and exponent with }2
16
x=\frac{0\pm 16}{4}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{0+16}{4}\\&x=\frac{0-16}{4}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{0+16}{4}
Simplify
More Steps
Evaluate
\frac{0+16}{4}
Removing 0 doesn't change the value,so remove it from the expression
\frac{16}{4}
Reduce the numbers
\frac{4}{1}
Calculate
4
x=4
\begin{align}&x=4\\&x=\frac{0-16}{4}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{0-16}{4}
Simplify
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Evaluate
\frac{0-16}{4}
Removing 0 doesn't change the value,so remove it from the expression
\frac{-16}{4}
Reduce the numbers
\frac{-4}{1}
Calculate
-4
x=-4
\begin{align}&x=4\\&x=-4\end{align}
Solution
x_{1}=-4,x_{2}=4
x_{1}=-4,x_{2}=4
Evaluate
2x^{2}+12=44
Move the expression to the left side
2x^{2}-32=0
Divide both sides
x^{2}-16=0
Solve using the PQ formula
x=\frac{0}{2}\pm \sqrt{\left(\frac{0}{2}\right)^{2}-\left(-16\right)}
Simplify the expression
More Steps
Evaluate
\left(\frac{0}{2}\right)^{2}-\left(-16\right)
Divide the terms
0^{2}-\left(-16\right)
Calculate
0-\left(-16\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
0+16
Removing 0 doesn't change the value,so remove it from the expression
16
x=\frac{0}{2}\pm \sqrt{16}
Simplify the expression
More Steps
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{0}{2}\pm 4
Divide the terms
x=0\pm 4
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=0+4\\&x=0-4\end{align}
Removing 0 doesn't change the value,so remove it from the expression
\begin{align}&x=4\\&x=0-4\end{align}
Removing 0 doesn't change the value,so remove it from the expression
\begin{align}&x=4\\&x=-4\end{align}
Solution
x_{1}=-4,x_{2}=4
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