(5x)(x+5)40=180

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Solution for (5x)(x+5)40=180 equation:


Simplifying
(5x)(x + 5) * 40 = 180

Remove parenthesis around (5x)
5x(x + 5) * 40 = 180

Reorder the terms:
5x(5 + x) * 40 = 180

Reorder the terms for easier multiplication:
5 * 40x(5 + x) = 180

Multiply 5 * 40
200x(5 + x) = 180
(5 * 200x + x * 200x) = 180
(1000x + 200x2) = 180

Solving
1000x + 200x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 1000x + 200x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 1000x + 200x2 = 0

Factor out the Greatest Common Factor (GCF), '20'.
20(-9 + 50x + 10x2) = 0

Ignore the factor 20.

Subproblem 1

Set the factor '(-9 + 50x + 10x2)' equal to zero and attempt to solve: Simplifying -9 + 50x + 10x2 = 0 Solving -9 + 50x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.9 + 5x + x2 = 0.0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 5x + 0.9 + x2 = 0.0 + 0.9 Reorder the terms: -0.9 + 0.9 + 5x + x2 = 0.0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 5x + x2 = 0.0 + 0.9 5x + x2 = 0.0 + 0.9 Combine like terms: 0.0 + 0.9 = 0.9 5x + x2 = 0.9 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 0.9 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 0.9 + 6.25 Combine like terms: 0.9 + 6.25 = 7.15 6.25 + 5x + x2 = 7.15 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 7.15 Calculate the square root of the right side: 2.673948391 Break this problem into two subproblems by setting (x + 2.5) equal to 2.673948391 and -2.673948391.

Subproblem 1

x + 2.5 = 2.673948391 Simplifying x + 2.5 = 2.673948391 Reorder the terms: 2.5 + x = 2.673948391 Solving 2.5 + x = 2.673948391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.673948391 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.673948391 + -2.5 x = 2.673948391 + -2.5 Combine like terms: 2.673948391 + -2.5 = 0.173948391 x = 0.173948391 Simplifying x = 0.173948391

Subproblem 2

x + 2.5 = -2.673948391 Simplifying x + 2.5 = -2.673948391 Reorder the terms: 2.5 + x = -2.673948391 Solving 2.5 + x = -2.673948391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.673948391 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.673948391 + -2.5 x = -2.673948391 + -2.5 Combine like terms: -2.673948391 + -2.5 = -5.173948391 x = -5.173948391 Simplifying x = -5.173948391

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.173948391, -5.173948391}

Solution

x = {0.173948391, -5.173948391}

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