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Simplifying 2x(x + 75) = 180 Reorder the terms: 2x(75 + x) = 180 (75 * 2x + x * 2x) = 180 (150x + 2x2) = 180 Solving 150x + 2x2 = 180 Solving for variable 'x'. Reorder the terms: -180 + 150x + 2x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 150x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-90 + 75x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-90 + 75x + x2)' equal to zero and attempt to solve: Simplifying -90 + 75x + x2 = 0 Solving -90 + 75x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 75x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 75x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 75x + x2 = 0 + 90 75x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 75x + x2 = 90 The x term is 75x. Take half its coefficient (37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. 75x + 1406.25 + x2 = 90 + 1406.25 Reorder the terms: 1406.25 + 75x + x2 = 90 + 1406.25 Combine like terms: 90 + 1406.25 = 1496.25 1406.25 + 75x + x2 = 1496.25 Factor a perfect square on the left side: (x + 37.5)(x + 37.5) = 1496.25 Calculate the square root of the right side: 38.681390875 Break this problem into two subproblems by setting (x + 37.5) equal to 38.681390875 and -38.681390875.Subproblem 1
x + 37.5 = 38.681390875 Simplifying x + 37.5 = 38.681390875 Reorder the terms: 37.5 + x = 38.681390875 Solving 37.5 + x = 38.681390875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = 38.681390875 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = 38.681390875 + -37.5 x = 38.681390875 + -37.5 Combine like terms: 38.681390875 + -37.5 = 1.181390875 x = 1.181390875 Simplifying x = 1.181390875Subproblem 2
x + 37.5 = -38.681390875 Simplifying x + 37.5 = -38.681390875 Reorder the terms: 37.5 + x = -38.681390875 Solving 37.5 + x = -38.681390875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37.5' to each side of the equation. 37.5 + -37.5 + x = -38.681390875 + -37.5 Combine like terms: 37.5 + -37.5 = 0.0 0.0 + x = -38.681390875 + -37.5 x = -38.681390875 + -37.5 Combine like terms: -38.681390875 + -37.5 = -76.181390875 x = -76.181390875 Simplifying x = -76.181390875Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.181390875, -76.181390875}Solution
x = {1.181390875, -76.181390875}
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