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Simplifying 36x2 + 720x + -48 = 0 Reorder the terms: -48 + 720x + 36x2 = 0 Solving -48 + 720x + 36x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '12'. 12(-4 + 60x + 3x2) = 0 Ignore the factor 12.Subproblem 1
Set the factor '(-4 + 60x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + 60x + 3x2 = 0 Solving -4 + 60x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + 20x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + 20x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + 20x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + 20x + x2 = 0 + 1.333333333 20x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 20x + x2 = 1.333333333 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 = 1.333333333 + 100 Reorder the terms: 100 + 20x + x2 = 1.333333333 + 100 Combine like terms: 1.333333333 + 100 = 101.333333333 100 + 20x + x2 = 101.333333333 Factor a perfect square on the left side: (x + 10)(x + 10) = 101.333333333 Calculate the square root of the right side: 10.066445914 Break this problem into two subproblems by setting (x + 10) equal to 10.066445914 and -10.066445914.Subproblem 1
x + 10 = 10.066445914 Simplifying x + 10 = 10.066445914 Reorder the terms: 10 + x = 10.066445914 Solving 10 + x = 10.066445914 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 = 10.066445914 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.066445914 + -10 x = 10.066445914 + -10 Combine like terms: 10.066445914 + -10 = 0.066445914 x = 0.066445914 Simplifying x = 0.066445914Subproblem 2
x + 10 = -10.066445914 Simplifying x + 10 = -10.066445914 Reorder the terms: 10 + x = -10.066445914 Solving 10 + x = -10.066445914 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 = -10.066445914 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.066445914 + -10 x = -10.066445914 + -10 Combine like terms: -10.066445914 + -10 = -20.066445914 x = -20.066445914 Simplifying x = -20.066445914Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.066445914, -20.066445914}Solution
x = {0.066445914, -20.066445914}
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