Question

Solve x²+ 8x- 6=0 using the Quadratic Formula.​

Answer 1

Answer:

The first term is, x2 its coefficient is 1 .

The middle term is, -8x its coefficient is -8 .

The last term, "the constant", is +6

Step-1 : Multiply the coefficient of the first term by the constant 1 • 6 = 6

Step-2 : Find two factors of 6 whose sum equals the coefficient of the middle term, which is -8 .

-6 + -1 = -7

-3 + -2 = -5

-2 + -3 = -5

-1 + -6 = -7

1 + 6 = 7

2 + 3 = 5

3 + 2 = 5

6 + 1 = 7

Observation : No two such factors can be found !!

Answer 2

⛥Required AnswèR :

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

⛥Explanation:

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

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

when  $\sf{ax^2 + bx + c = 0}$

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

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

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

•Substitute the values into the formula.

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

✰Solve inside the radical first.

→Solve the exponent.

8²= 8×8= 64

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

⛥Multiply 4, 1, and -6.

4(1)(-6)= 4(-6)= -24

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

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

64- 24 64+24=88

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

⛥Solve the denominator.

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

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

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

⛥Take the square root of 4.

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

✰Divide by 2.

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

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

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