5(5-2x-2x+2)(9x+9)=27

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Solution for 5(5-2x-2x+2)(9x+9)=27 equation:


Simplifying
5(5 + -2x + -2x + 2)(9x + 9) = 27

Reorder the terms:
5(5 + 2 + -2x + -2x)(9x + 9) = 27

Combine like terms: 5 + 2 = 7
5(7 + -2x + -2x)(9x + 9) = 27

Combine like terms: -2x + -2x = -4x
5(7 + -4x)(9x + 9) = 27

Reorder the terms:
5(7 + -4x)(9 + 9x) = 27

Multiply (7 + -4x) * (9 + 9x)
5(7(9 + 9x) + -4x * (9 + 9x)) = 27
5((9 * 7 + 9x * 7) + -4x * (9 + 9x)) = 27
5((63 + 63x) + -4x * (9 + 9x)) = 27
5(63 + 63x + (9 * -4x + 9x * -4x)) = 27
5(63 + 63x + (-36x + -36x2)) = 27

Combine like terms: 63x + -36x = 27x
5(63 + 27x + -36x2) = 27
(63 * 5 + 27x * 5 + -36x2 * 5) = 27
(315 + 135x + -180x2) = 27

Solving
315 + 135x + -180x2 = 27

Solving for variable 'x'.

Reorder the terms:
315 + -27 + 135x + -180x2 = 27 + -27

Combine like terms: 315 + -27 = 288
288 + 135x + -180x2 = 27 + -27

Combine like terms: 27 + -27 = 0
288 + 135x + -180x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(32 + 15x + -20x2) = 0

Ignore the factor 9.

Subproblem 1

Set the factor '(32 + 15x + -20x2)' equal to zero and attempt to solve: Simplifying 32 + 15x + -20x2 = 0 Solving 32 + 15x + -20x2 = 0 Begin completing the square. Divide all terms by -20 the coefficient of the squared term: Divide each side by '-20'. -1.6 + -0.75x + x2 = 0.0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + -0.75x + 1.6 + x2 = 0.0 + 1.6 Reorder the terms: -1.6 + 1.6 + -0.75x + x2 = 0.0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + -0.75x + x2 = 0.0 + 1.6 -0.75x + x2 = 0.0 + 1.6 Combine like terms: 0.0 + 1.6 = 1.6 -0.75x + x2 = 1.6 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 1.6 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 1.6 + 0.140625 Combine like terms: 1.6 + 0.140625 = 1.740625 0.140625 + -0.75x + x2 = 1.740625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 1.740625 Calculate the square root of the right side: 1.31932748 Break this problem into two subproblems by setting (x + -0.375) equal to 1.31932748 and -1.31932748.

Subproblem 1

x + -0.375 = 1.31932748 Simplifying x + -0.375 = 1.31932748 Reorder the terms: -0.375 + x = 1.31932748 Solving -0.375 + x = 1.31932748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.31932748 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.31932748 + 0.375 x = 1.31932748 + 0.375 Combine like terms: 1.31932748 + 0.375 = 1.69432748 x = 1.69432748 Simplifying x = 1.69432748

Subproblem 2

x + -0.375 = -1.31932748 Simplifying x + -0.375 = -1.31932748 Reorder the terms: -0.375 + x = -1.31932748 Solving -0.375 + x = -1.31932748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.31932748 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.31932748 + 0.375 x = -1.31932748 + 0.375 Combine like terms: -1.31932748 + 0.375 = -0.94432748 x = -0.94432748 Simplifying x = -0.94432748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.69432748, -0.94432748}

Solution

x = {1.69432748, -0.94432748}

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