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Question
-4x^{2}+4x+7=0
Solve the quadratic equation
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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
x_{1}=\frac{1-2\sqrt{2}}{2},x_{2}=\frac{1+2\sqrt{2}}{2}
Alternative Form
x_{1}\approx -0.914214,x_{2}\approx 1.914214
Evaluate
-4x^{2}+4x+7=0
Multiply both sides
4x^{2}-4x-7=0
\text{Substitute a=}4\text{,b=}-4\text{ and c=}-7\text{ into the quadratic formula }x\text{=}\frac{-b\pm\sqrt{b^2-4ac}}{2a}
x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 4\left(-7\right)}}{2\times 4}
Simplify the expression
x=\frac{4\pm \sqrt{\left(-4\right)^{2}-4\times 4\left(-7\right)}}{8}
Simplify the expression
More Steps
Evaluate
\left(-4\right)^{2}-4\times 4\left(-7\right)
Multiply
More Steps
Multiply the terms
4\times 4\left(-7\right)
Rewrite the expression
-4\times 4\times 7
Multiply the terms
-112
\left(-4\right)^{2}-\left(-112\right)
Rewrite the expression
4^{2}-\left(-112\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
4^{2}+112
Evaluate the power
16+112
Add the numbers
128
x=\frac{4\pm \sqrt{128}}{8}
Simplify the radical expression
More Steps
Evaluate
\sqrt{128}
Write the expression as a product where the root of one of the factors can be evaluated
\sqrt{64\times 2}
\text{Write the number in exponential form with the base of }8
\sqrt{8^{2}\times 2}
The root of a product is equal to the product of the roots of each factor
\sqrt{8^{2}}\times \sqrt{2}
\text{Reduce the index of the radical and exponent with }2
8\sqrt{2}
x=\frac{4\pm 8\sqrt{2}}{8}
\text{Separate the equation into }2\text{ possible cases}
\begin{align}&x=\frac{4+8\sqrt{2}}{8}\\&x=\frac{4-8\sqrt{2}}{8}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{4+8\sqrt{2}}{8}
Divide the terms
More Steps
Evaluate
\frac{4+8\sqrt{2}}{8}
Rewrite the expression
\frac{4\left(1+2\sqrt{2}\right)}{8}
\text{Cancel out the common factor }4
\frac{1+2\sqrt{2}}{2}
x=\frac{1+2\sqrt{2}}{2}
\begin{align}&x=\frac{1+2\sqrt{2}}{2}\\&x=\frac{4-8\sqrt{2}}{8}\end{align}
Simplify the expression
More Steps
Evaluate
x=\frac{4-8\sqrt{2}}{8}
Divide the terms
More Steps
Evaluate
\frac{4-8\sqrt{2}}{8}
Rewrite the expression
\frac{4\left(1-2\sqrt{2}\right)}{8}
\text{Cancel out the common factor }4
\frac{1-2\sqrt{2}}{2}
x=\frac{1-2\sqrt{2}}{2}
\begin{align}&x=\frac{1+2\sqrt{2}}{2}\\&x=\frac{1-2\sqrt{2}}{2}\end{align}
Solution
x_{1}=\frac{1-2\sqrt{2}}{2},x_{2}=\frac{1+2\sqrt{2}}{2}
Alternative Form
x_{1}\approx -0.914214,x_{2}\approx 1.914214
Show Solutions
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