4x(x+8)=(7x-16)

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Solution for 4x(x+8)=(7x-16) equation:


Simplifying
4x(x + 8) = (7x + -16)

Reorder the terms:
4x(8 + x) = (7x + -16)
(8 * 4x + x * 4x) = (7x + -16)
(32x + 4x2) = (7x + -16)

Reorder the terms:
32x + 4x2 = (-16 + 7x)

Remove parenthesis around (-16 + 7x)
32x + 4x2 = -16 + 7x

Solving
32x + 4x2 = -16 + 7x

Solving for variable 'x'.

Reorder the terms:
16 + 32x + -7x + 4x2 = -16 + 7x + 16 + -7x

Combine like terms: 32x + -7x = 25x
16 + 25x + 4x2 = -16 + 7x + 16 + -7x

Reorder the terms:
16 + 25x + 4x2 = -16 + 16 + 7x + -7x

Combine like terms: -16 + 16 = 0
16 + 25x + 4x2 = 0 + 7x + -7x
16 + 25x + 4x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
16 + 25x + 4x2 = 0

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

Divide each side by '4'.
4 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6.25x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 6.25x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6.25x + x2 = 0 + -4
6.25x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
6.25x + x2 = -4

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -4 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -4 + 9.765625

Combine like terms: -4 + 9.765625 = 5.765625
9.765625 + 6.25x + x2 = 5.765625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.401171589 and -2.401171589.

Subproblem 1

x + 3.125 = 2.401171589 Simplifying x + 3.125 = 2.401171589 Reorder the terms: 3.125 + x = 2.401171589 Solving 3.125 + x = 2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = 2.401171589 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = 2.401171589 + -3.125 x = 2.401171589 + -3.125 Combine like terms: 2.401171589 + -3.125 = -0.723828411 x = -0.723828411 Simplifying x = -0.723828411

Subproblem 2

x + 3.125 = -2.401171589 Simplifying x + 3.125 = -2.401171589 Reorder the terms: 3.125 + x = -2.401171589 Solving 3.125 + x = -2.401171589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.125' to each side of the equation. 3.125 + -3.125 + x = -2.401171589 + -3.125 Combine like terms: 3.125 + -3.125 = 0.000 0.000 + x = -2.401171589 + -3.125 x = -2.401171589 + -3.125 Combine like terms: -2.401171589 + -3.125 = -5.526171589 x = -5.526171589 Simplifying x = -5.526171589

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.723828411, -5.526171589}

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