(x-8)(x+9)=7

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Solution for (x-8)(x+9)=7 equation:


Simplifying
(x + -8)(x + 9) = 7

Reorder the terms:
(-8 + x)(x + 9) = 7

Reorder the terms:
(-8 + x)(9 + x) = 7

Multiply (-8 + x) * (9 + x)
(-8(9 + x) + x(9 + x)) = 7
((9 * -8 + x * -8) + x(9 + x)) = 7
((-72 + -8x) + x(9 + x)) = 7
(-72 + -8x + (9 * x + x * x)) = 7
(-72 + -8x + (9x + x2)) = 7

Combine like terms: -8x + 9x = 1x
(-72 + 1x + x2) = 7

Solving
-72 + 1x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-72 + -7 + 1x + x2 = 7 + -7

Combine like terms: -72 + -7 = -79
-79 + 1x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-79 + 1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '79' to each side of the equation.
-79 + 1x + 79 + x2 = 0 + 79

Reorder the terms:
-79 + 79 + 1x + x2 = 0 + 79

Combine like terms: -79 + 79 = 0
0 + 1x + x2 = 0 + 79
1x + x2 = 0 + 79

Combine like terms: 0 + 79 = 79
1x + x2 = 79

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 79 + 0.25

Reorder the terms:
0.25 + x + x2 = 79 + 0.25

Combine like terms: 79 + 0.25 = 79.25
0.25 + x + x2 = 79.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(x + 0.5) equal to 8.902246907 and -8.902246907.

Subproblem 1

x + 0.5 = 8.902246907 Simplifying x + 0.5 = 8.902246907 Reorder the terms: 0.5 + x = 8.902246907 Solving 0.5 + x = 8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 8.902246907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.902246907 + -0.5 x = 8.902246907 + -0.5 Combine like terms: 8.902246907 + -0.5 = 8.402246907 x = 8.402246907 Simplifying x = 8.402246907

Subproblem 2

x + 0.5 = -8.902246907 Simplifying x + 0.5 = -8.902246907 Reorder the terms: 0.5 + x = -8.902246907 Solving 0.5 + x = -8.902246907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -8.902246907 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.902246907 + -0.5 x = -8.902246907 + -0.5 Combine like terms: -8.902246907 + -0.5 = -9.402246907 x = -9.402246907 Simplifying x = -9.402246907

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.402246907, -9.402246907}

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