(4x+9)(x-4)=16+36

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Solution for (4x+9)(x-4)=16+36 equation:


Simplifying
(4x + 9)(x + -4) = 16 + 36

Reorder the terms:
(9 + 4x)(x + -4) = 16 + 36

Reorder the terms:
(9 + 4x)(-4 + x) = 16 + 36

Multiply (9 + 4x) * (-4 + x)
(9(-4 + x) + 4x * (-4 + x)) = 16 + 36
((-4 * 9 + x * 9) + 4x * (-4 + x)) = 16 + 36
((-36 + 9x) + 4x * (-4 + x)) = 16 + 36
(-36 + 9x + (-4 * 4x + x * 4x)) = 16 + 36
(-36 + 9x + (-16x + 4x2)) = 16 + 36

Combine like terms: 9x + -16x = -7x
(-36 + -7x + 4x2) = 16 + 36

Combine like terms: 16 + 36 = 52
-36 + -7x + 4x2 = 52

Solving
-36 + -7x + 4x2 = 52

Solving for variable 'x'.

Reorder the terms:
-36 + -52 + -7x + 4x2 = 52 + -52

Combine like terms: -36 + -52 = -88
-88 + -7x + 4x2 = 52 + -52

Combine like terms: 52 + -52 = 0
-88 + -7x + 4x2 = 0

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

Divide each side by '4'.
-22 + -1.75x + x2 = 0

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -1.75x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -1.75x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1.75x + x2 = 0 + 22
-1.75x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-1.75x + x2 = 22

The x term is -1.75x.  Take half its coefficient (-0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
-1.75x + 0.765625 + x2 = 22 + 0.765625

Reorder the terms:
0.765625 + -1.75x + x2 = 22 + 0.765625

Combine like terms: 22 + 0.765625 = 22.765625
0.765625 + -1.75x + x2 = 22.765625

Factor a perfect square on the left side:
(x + -0.875)(x + -0.875) = 22.765625

Calculate the square root of the right side: 4.771333671

Break this problem into two subproblems by setting 
(x + -0.875) equal to 4.771333671 and -4.771333671.

Subproblem 1

x + -0.875 = 4.771333671 Simplifying x + -0.875 = 4.771333671 Reorder the terms: -0.875 + x = 4.771333671 Solving -0.875 + x = 4.771333671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 4.771333671 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 4.771333671 + 0.875 x = 4.771333671 + 0.875 Combine like terms: 4.771333671 + 0.875 = 5.646333671 x = 5.646333671 Simplifying x = 5.646333671

Subproblem 2

x + -0.875 = -4.771333671 Simplifying x + -0.875 = -4.771333671 Reorder the terms: -0.875 + x = -4.771333671 Solving -0.875 + x = -4.771333671 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -4.771333671 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -4.771333671 + 0.875 x = -4.771333671 + 0.875 Combine like terms: -4.771333671 + 0.875 = -3.896333671 x = -3.896333671 Simplifying x = -3.896333671

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.646333671, -3.896333671}

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