4x(2+2x-5)=37

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Solution for 4x(2+2x-5)=37 equation:


Simplifying
4x(2 + 2x + -5) = 37

Reorder the terms:
4x(2 + -5 + 2x) = 37

Combine like terms: 2 + -5 = -3
4x(-3 + 2x) = 37
(-3 * 4x + 2x * 4x) = 37
(-12x + 8x2) = 37

Solving
-12x + 8x2 = 37

Solving for variable 'x'.

Reorder the terms:
-37 + -12x + 8x2 = 37 + -37

Combine like terms: 37 + -37 = 0
-37 + -12x + 8x2 = 0

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

Divide each side by '8'.
-4.625 + -1.5x + x2 = 0

Move the constant term to the right:

Add '4.625' to each side of the equation.
-4.625 + -1.5x + 4.625 + x2 = 0 + 4.625

Reorder the terms:
-4.625 + 4.625 + -1.5x + x2 = 0 + 4.625

Combine like terms: -4.625 + 4.625 = 0.000
0.000 + -1.5x + x2 = 0 + 4.625
-1.5x + x2 = 0 + 4.625

Combine like terms: 0 + 4.625 = 4.625
-1.5x + x2 = 4.625

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 4.625 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 4.625 + 0.5625

Combine like terms: 4.625 + 0.5625 = 5.1875
0.5625 + -1.5x + x2 = 5.1875

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 5.1875

Calculate the square root of the right side: 2.277608395

Break this problem into two subproblems by setting 
(x + -0.75) equal to 2.277608395 and -2.277608395.

Subproblem 1

x + -0.75 = 2.277608395 Simplifying x + -0.75 = 2.277608395 Reorder the terms: -0.75 + x = 2.277608395 Solving -0.75 + x = 2.277608395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 2.277608395 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 2.277608395 + 0.75 x = 2.277608395 + 0.75 Combine like terms: 2.277608395 + 0.75 = 3.027608395 x = 3.027608395 Simplifying x = 3.027608395

Subproblem 2

x + -0.75 = -2.277608395 Simplifying x + -0.75 = -2.277608395 Reorder the terms: -0.75 + x = -2.277608395 Solving -0.75 + x = -2.277608395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -2.277608395 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -2.277608395 + 0.75 x = -2.277608395 + 0.75 Combine like terms: -2.277608395 + 0.75 = -1.527608395 x = -1.527608395 Simplifying x = -1.527608395

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.027608395, -1.527608395}

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