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Simplifying 2x(x + 60) = 180 Reorder the terms: 2x(60 + x) = 180 (60 * 2x + x * 2x) = 180 (120x + 2x2) = 180 Solving 120x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 120x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 120x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 60x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 60x + x2)' equal to zero and attempt to solve: Simplifying -90 + 60x + x2 = 0 Solving -90 + 60x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 60x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 60x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 60x + x2 = 0 + 90 60x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 60x + x2 = 90 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = 90 + 900 Reorder the terms: 900 + 60x + x2 = 90 + 900 Combine like terms: 90 + 900 = 990 900 + 60x + x2 = 990 Factor a perfect square on the left side: (x + 30)(x + 30) = 990 Calculate the square root of the right side: 31.464265445 Break this problem into two subproblems by setting (x + 30) equal to 31.464265445 and -31.464265445.Subproblem 1
x + 30 = 31.464265445 Simplifying x + 30 = 31.464265445 Reorder the terms: 30 + x = 31.464265445 Solving 30 + x = 31.464265445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 31.464265445 + -30 Combine like terms: 30 + -30 = 0 0 + x = 31.464265445 + -30 x = 31.464265445 + -30 Combine like terms: 31.464265445 + -30 = 1.464265445 x = 1.464265445 Simplifying x = 1.464265445Subproblem 2
x + 30 = -31.464265445 Simplifying x + 30 = -31.464265445 Reorder the terms: 30 + x = -31.464265445 Solving 30 + x = -31.464265445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -31.464265445 + -30 Combine like terms: 30 + -30 = 0 0 + x = -31.464265445 + -30 x = -31.464265445 + -30 Combine like terms: -31.464265445 + -30 = -61.464265445 x = -61.464265445 Simplifying x = -61.464265445Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.464265445, -61.464265445}Solution
x = {1.464265445, -61.464265445}
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