Question

Solve x^2+ 8x- 6=0 using the Quadratic Formula

Answer 1

Answer:

x=−4+√22 or x=−4−√22

Step-by-step explanation:

Substitute all values in the quadratic formula.

Solve.

Answer 2

Answer:

$\boxed {\sf x= {{ - 4\pm \sqrt{22} }}}$

Step-by-step explanation:

The quadratic equation is used to find the roots of a quadratic. The formula is:

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

when  ${ax^2 + bx + c = 0}$

We are given the quadratic: $x^2+8x-6=0$

If we compare the given quadratic to the standard form of a quadratic, then:

$a= 1\\b=8 \\c= -6$

Substitute the values into the formula.

$x = \frac{{ - 8\pm \sqrt {8^2 - 4(1)(-6)} }}{{2(1)}}$

Solve inside the radical first.

Solve the exponent.

• 8²= 8*8= 64

$x = \frac{{ - 8\pm \sqrt {64 - 4(1)(-6)} }}{{2(1)}}$

Multiply 4, 1, and -6.

• 4(1)(-6)= 4(-6)= -24

$x = \frac{{ - 8\pm \sqrt {64 - -24}}}{{2(1)}}$

Add 64 and 24 (2 negative signs become a positive)

• 64- -24 64+24=88

$x = \frac{{ - 8\pm \sqrt {88}}}{{2(1)}}$

Solve the denominator.

$x = \frac{{ - 8\pm \sqrt {88}}}{{2}}$

The radical can be simplified. 88 is divisible by a perfect square: 4

$x= \frac{{ - 8\pm \sqrt {4}\sqrt{22} }}{{2}}$

Take the square root of 4.

$x= \frac{{ - 8\pm 2\sqrt{22} }}{{2}}$

Divide by 2.

$x= {{ - 4\pm \sqrt{22} }}$

The roots are: x=0.690416  and x=−8.69042