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Simplifying 12x2 + -180x + 500 = 0 Reorder the terms: 500 + -180x + 12x2 = 0 Solving 500 + -180x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(125 + -45x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(125 + -45x + 3x2)' equal to zero and attempt to solve: Simplifying 125 + -45x + 3x2 = 0 Solving 125 + -45x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 41.66666667 + -15x + x2 = 0 Move the constant term to the right: Add '-41.66666667' to each side of the equation. 41.66666667 + -15x + -41.66666667 + x2 = 0 + -41.66666667 Reorder the terms: 41.66666667 + -41.66666667 + -15x + x2 = 0 + -41.66666667 Combine like terms: 41.66666667 + -41.66666667 = 0.00000000 0.00000000 + -15x + x2 = 0 + -41.66666667 -15x + x2 = 0 + -41.66666667 Combine like terms: 0 + -41.66666667 = -41.66666667 -15x + x2 = -41.66666667 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -41.66666667 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -41.66666667 + 56.25 Combine like terms: -41.66666667 + 56.25 = 14.58333333 56.25 + -15x + x2 = 14.58333333 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 14.58333333 Calculate the square root of the right side: 3.818813079 Break this problem into two subproblems by setting (x + -7.5) equal to 3.818813079 and -3.818813079.Subproblem 1
x + -7.5 = 3.818813079 Simplifying x + -7.5 = 3.818813079 Reorder the terms: -7.5 + x = 3.818813079 Solving -7.5 + x = 3.818813079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 3.818813079 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 3.818813079 + 7.5 x = 3.818813079 + 7.5 Combine like terms: 3.818813079 + 7.5 = 11.318813079 x = 11.318813079 Simplifying x = 11.318813079Subproblem 2
x + -7.5 = -3.818813079 Simplifying x + -7.5 = -3.818813079 Reorder the terms: -7.5 + x = -3.818813079 Solving -7.5 + x = -3.818813079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -3.818813079 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -3.818813079 + 7.5 x = -3.818813079 + 7.5 Combine like terms: -3.818813079 + 7.5 = 3.681186921 x = 3.681186921 Simplifying x = 3.681186921Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.318813079, 3.681186921}Solution
x = {11.318813079, 3.681186921}
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