(x+4)(x-5)=7

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Solution for (x+4)(x-5)=7 equation:


Simplifying
(x + 4)(x + -5) = 7

Reorder the terms:
(4 + x)(x + -5) = 7

Reorder the terms:
(4 + x)(-5 + x) = 7

Multiply (4 + x) * (-5 + x)
(4(-5 + x) + x(-5 + x)) = 7
((-5 * 4 + x * 4) + x(-5 + x)) = 7
((-20 + 4x) + x(-5 + x)) = 7
(-20 + 4x + (-5 * x + x * x)) = 7
(-20 + 4x + (-5x + x2)) = 7

Combine like terms: 4x + -5x = -1x
(-20 + -1x + x2) = 7

Solving
-20 + -1x + x2 = 7

Solving for variable 'x'.

Reorder the terms:
-20 + -7 + -1x + x2 = 7 + -7

Combine like terms: -20 + -7 = -27
-27 + -1x + x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-27 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -1x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -1x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -1x + x2 = 0 + 27
-1x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-1x + x2 = 27

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.
-1x + 0.25 + x2 = 27 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 27 + 0.25

Combine like terms: 27 + 0.25 = 27.25
0.25 + -1x + x2 = 27.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

x + -0.5 = 5.220153254 Simplifying x + -0.5 = 5.220153254 Reorder the terms: -0.5 + x = 5.220153254 Solving -0.5 + x = 5.220153254 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 = 5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 5.220153254 + 0.5 x = 5.220153254 + 0.5 Combine like terms: 5.220153254 + 0.5 = 5.720153254 x = 5.720153254 Simplifying x = 5.720153254

Subproblem 2

x + -0.5 = -5.220153254 Simplifying x + -0.5 = -5.220153254 Reorder the terms: -0.5 + x = -5.220153254 Solving -0.5 + x = -5.220153254 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 = -5.220153254 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -5.220153254 + 0.5 x = -5.220153254 + 0.5 Combine like terms: -5.220153254 + 0.5 = -4.720153254 x = -4.720153254 Simplifying x = -4.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.720153254, -4.720153254}

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