Solve by Completing the Square -x^2+8x-6=0

$- x^{2} + 8 x - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$- x^{2} + 8 x = 6$

Step 2

Divide each term in $- x^{2} + 8 x = 6$ by $- 1$ and simplify.

Divide each term in $- x^{2} + 8 x = 6$ by $- 1$ .

$\frac{- x^{2}}{- 1} + \frac{8 x}{- 1} = \frac{6}{- 1}$

Simplify the left side.

Simplify each term.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} + \frac{8 x}{- 1} = \frac{6}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} + \frac{8 x}{- 1} = \frac{6}{- 1}$

Move the negative one from the denominator of $\frac{8 x}{- 1}$ .

$x^{2} - 1 \cdot (8 x) = \frac{6}{- 1}$

Rewrite $- 1 \cdot (8 x)$ as $- (8 x)$ .

$x^{2} - (8 x) = \frac{6}{- 1}$

Multiply $8$ by $- 1$ .

$x^{2} - 8 x = \frac{6}{- 1}$

Simplify the right side.

Divide $6$ by $- 1$ .

$x^{2} - 8 x = - 6$

Step 3

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 4)}^{2}$

Step 4

Add the term to each side of the equation.

$x^{2} - 8 x + {(- 4)}^{2} = - 6 + {(- 4)}^{2}$

Step 5

Simplify the equation.

Simplify the left side.

Raise $- 4$ to the power of $2$ .

$x^{2} - 8 x + 16 = - 6 + {(- 4)}^{2}$

Simplify the right side.

Simplify $- 6 + {(- 4)}^{2}$ .

Raise $- 4$ to the power of $2$ .

$x^{2} - 8 x + 16 = - 6 + 16$

Add $- 6$ and $16$ .

$x^{2} - 8 x + 16 = 10$

Step 6

Factor the perfect trinomial square into ${(x - 4)}^{2}$ .

${(x - 4)}^{2} = 10$

Step 7

Solve the equation for $x$ .

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x - 4 = \pm \sqrt{10}$

Add $4$ to both sides of the equation.

$x = \pm \sqrt{10} + 4$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{10} + 4$

Decimal Form:

$x = 7.16227766 \dots, 0.83772233 \dots$

Solve by Completing the Square -x^2+8x-6=0

Related Questions

Support LCMGCF.com by disabling your adblocker.