Solve Using the Quadratic Formula x^2-8x-7=0

Problem

$x^2-8x-7=0$

Solution

1. Identify the coefficients $a$ $b$ and $c$ from the quadratic equation in the form $a{x}^2+bx+c=0$

$a=1$

$b=-8$

$c=-7$

2. State the quadratic formula used to find the roots of the equation.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

3. Substitute the values of $a$ $b$ and $c$ into the formula.

$x=\frac{-(-8)\pm \sqrt{{(-8)}^2-4\left(1\right)(-7)}}{2\left(1\right)}$

4. Simplify the expression inside the square root (the discriminant).

$x=\frac{8\pm \sqrt{64+28}}{2}$

$x=\frac{8\pm \sqrt{92}}{2}$

5. Simplify the radical by factoring out the largest perfect square.

$x=\frac{8\pm \sqrt{4\cdot 23}}{2}$

$x=\frac{8\pm 2\sqrt{23}}{2}$

6. Divide each term in the numerator by the denominator to find the final values of $x$

$x=4\pm \sqrt{23}$

Final Answer

$x=4\pm \sqrt{23}$

Want more problems? Check here!