(2x)(5x+5)=180

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Solution for (2x)(5x+5)=180 equation:


Simplifying
(2x)(5x + 5) = 180

Remove parenthesis around (2x)
2x(5x + 5) = 180

Reorder the terms:
2x(5 + 5x) = 180
(5 * 2x + 5x * 2x) = 180
(10x + 10x2) = 180

Solving
10x + 10x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 10x + 10x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 10x + 10x2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-18 + x + x2) = 0

Ignore the factor 10.

Subproblem 1

Set the factor '(-18 + x + x2)' equal to zero and attempt to solve: Simplifying -18 + x + x2 = 0 Solving -18 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + x + x2 = 0 + 18 x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 x + x2 = 18 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. x + 0.25 + x2 = 18 + 0.25 Reorder the terms: 0.25 + x + x2 = 18 + 0.25 Combine like terms: 18 + 0.25 = 18.25 0.25 + x + x2 = 18.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + 0.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 0.5 = 4.272001873 Simplifying x + 0.5 = 4.272001873 Reorder the terms: 0.5 + x = 4.272001873 Solving 0.5 + x = 4.272001873 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 = 4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.272001873 + -0.5 x = 4.272001873 + -0.5 Combine like terms: 4.272001873 + -0.5 = 3.772001873 x = 3.772001873 Simplifying x = 3.772001873

Subproblem 2

x + 0.5 = -4.272001873 Simplifying x + 0.5 = -4.272001873 Reorder the terms: 0.5 + x = -4.272001873 Solving 0.5 + x = -4.272001873 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 = -4.272001873 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.272001873 + -0.5 x = -4.272001873 + -0.5 Combine like terms: -4.272001873 + -0.5 = -4.772001873 x = -4.772001873 Simplifying x = -4.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.772001873, -4.772001873}

Solution

x = {3.772001873, -4.772001873}

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