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Simplifying 60x = 3x2 + 36 Reorder the terms: 60x = 36 + 3x2 Solving 60x = 36 + 3x2 Solving for variable 'x'. Reorder the terms: -36 + 60x + -3x2 = 36 + 3x2 + -36 + -3x2 Reorder the terms: -36 + 60x + -3x2 = 36 + -36 + 3x2 + -3x2 Combine like terms: 36 + -36 = 0 -36 + 60x + -3x2 = 0 + 3x2 + -3x2 -36 + 60x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -36 + 60x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 20x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 20x + -1x2)' equal to zero and attempt to solve: Simplifying -12 + 20x + -1x2 = 0 Solving -12 + 20x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 12 + -20x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -20x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -20x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -20x + x2 = 0 + -12 -20x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -20x + x2 = -12 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 = -12 + 100 Reorder the terms: 100 + -20x + x2 = -12 + 100 Combine like terms: -12 + 100 = 88 100 + -20x + x2 = 88 Factor a perfect square on the left side: (x + -10)(x + -10) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + -10) equal to 9.38083152 and -9.38083152.Subproblem 1
x + -10 = 9.38083152 Simplifying x + -10 = 9.38083152 Reorder the terms: -10 + x = 9.38083152 Solving -10 + x = 9.38083152 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 = 9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.38083152 + 10 x = 9.38083152 + 10 Combine like terms: 9.38083152 + 10 = 19.38083152 x = 19.38083152 Simplifying x = 19.38083152Subproblem 2
x + -10 = -9.38083152 Simplifying x + -10 = -9.38083152 Reorder the terms: -10 + x = -9.38083152 Solving -10 + x = -9.38083152 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 = -9.38083152 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.38083152 + 10 x = -9.38083152 + 10 Combine like terms: -9.38083152 + 10 = 0.61916848 x = 0.61916848 Simplifying x = 0.61916848Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.38083152, 0.61916848}Solution
x = {19.38083152, 0.61916848}
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