-x^2+8x=-7

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Solution for -x^2+8x=-7 equation:


Simplifying
-1x2 + 8x = -7

Reorder the terms:
8x + -1x2 = -7

Solving
8x + -1x2 = -7

Solving for variable 'x'.

Reorder the terms:
7 + 8x + -1x2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -8x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -8x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -8x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -8x + x2 = 0 + 7
-8x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-8x + x2 = 7

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 7 + 16

Reorder the terms:
16 + -8x + x2 = 7 + 16

Combine like terms: 7 + 16 = 23
16 + -8x + x2 = 23

Factor a perfect square on the left side:
(x + -4)(x + -4) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(x + -4) equal to 4.795831523 and -4.795831523.

Subproblem 1

x + -4 = 4.795831523 Simplifying x + -4 = 4.795831523 Reorder the terms: -4 + x = 4.795831523 Solving -4 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x = 4.795831523 + 4 x = 4.795831523 + 4 Combine like terms: 4.795831523 + 4 = 8.795831523 x = 8.795831523 Simplifying x = 8.795831523

Subproblem 2

x + -4 = -4.795831523 Simplifying x + -4 = -4.795831523 Reorder the terms: -4 + x = -4.795831523 Solving -4 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -4.795831523 + 4 Combine like terms: -4 + 4 = 0 0 + x = -4.795831523 + 4 x = -4.795831523 + 4 Combine like terms: -4.795831523 + 4 = -0.795831523 x = -0.795831523 Simplifying x = -0.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.795831523, -0.795831523}

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