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Simplifying 60 + (x + 20) * 3x = 180 Reorder the terms: 60 + (20 + x) * 3x = 180 Reorder the terms for easier multiplication: 60 + 3x(20 + x) = 180 60 + (20 * 3x + x * 3x) = 180 60 + (60x + 3x2) = 180 Solving 60 + 60x + 3x2 = 180 Solving for variable 'x'. Reorder the terms: 60 + -180 + 60x + 3x2 = 180 + -180 Combine like terms: 60 + -180 = -120 -120 + 60x + 3x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -120 + 60x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-40 + 20x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-40 + 20x + x2)' equal to zero and attempt to solve: Simplifying -40 + 20x + x2 = 0 Solving -40 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 20x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 20x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 20x + x2 = 0 + 40 20x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 20x + x2 = 40 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 40 + 100 Reorder the terms: 100 + 20x + x2 = 40 + 100 Combine like terms: 40 + 100 = 140 100 + 20x + x2 = 140 Factor a perfect square on the left side: (x + 10)(x + 10) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (x + 10) equal to 11.832159566 and -11.832159566.Subproblem 1
x + 10 = 11.832159566 Simplifying x + 10 = 11.832159566 Reorder the terms: 10 + x = 11.832159566 Solving 10 + x = 11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + x = 11.832159566 + -10 x = 11.832159566 + -10 Combine like terms: 11.832159566 + -10 = 1.832159566 x = 1.832159566 Simplifying x = 1.832159566Subproblem 2
x + 10 = -11.832159566 Simplifying x + 10 = -11.832159566 Reorder the terms: 10 + x = -11.832159566 Solving 10 + x = -11.832159566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -11.832159566 + -10 Combine like terms: 10 + -10 = 0 0 + x = -11.832159566 + -10 x = -11.832159566 + -10 Combine like terms: -11.832159566 + -10 = -21.832159566 x = -21.832159566 Simplifying x = -21.832159566Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.832159566, -21.832159566}Solution
x = {1.832159566, -21.832159566}
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