360=(5x+5)2x

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Solution for 360=(5x+5)2x equation:


Simplifying
360 = (5x + 5) * 2x

Reorder the terms:
360 = (5 + 5x) * 2x

Reorder the terms for easier multiplication:
360 = 2x(5 + 5x)
360 = (5 * 2x + 5x * 2x)
360 = (10x + 10x2)

Solving
360 = 10x + 10x2

Solving for variable 'x'.

Reorder the terms:
360 + -10x + -10x2 = 10x + -10x + 10x2 + -10x2

Combine like terms: 10x + -10x = 0
360 + -10x + -10x2 = 0 + 10x2 + -10x2
360 + -10x + -10x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
360 + -10x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(36 + -1x + -1x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(36 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 36 + -1x + -1x2 = 0 Solving 36 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + x + x2 = 0 + 36 x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 x + x2 = 36 The x term is x. 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. + 0.25 + x2 = 36 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 36 + 0.25 Combine like terms: 36 + 0.25 = 36.25 1.25 + x2 = 36.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 36.25 Calculate the square root of the right side: 6.020797289 Break this problem into two subproblems by setting (x + 0.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

x + 0.5 = 6.020797289 Simplifying x + 0.5 = 6.020797289 Reorder the terms: 0.5 + x = 6.020797289 Solving 0.5 + x = 6.020797289 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 = 6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.020797289 + -0.5 x = 6.020797289 + -0.5 Combine like terms: 6.020797289 + -0.5 = 5.520797289 x = 5.520797289 Simplifying x = 5.520797289

Subproblem 2

x + 0.5 = -6.020797289 Simplifying x + 0.5 = -6.020797289 Reorder the terms: 0.5 + x = -6.020797289 Solving 0.5 + x = -6.020797289 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 = -6.020797289 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.020797289 + -0.5 x = -6.020797289 + -0.5 Combine like terms: -6.020797289 + -0.5 = -6.520797289 x = -6.520797289 Simplifying x = -6.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.520797289, -6.520797289}

Solution

x = {5.520797289, -6.520797289}

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