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Simplifying 0 = 2x2 + -36x + -72 Reorder the terms: 0 = -72 + -36x + 2x2 Solving 0 = -72 + -36x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 72 = 72 72 + 36x + -2x2 = -72 + -36x + 2x2 + 72 + 36x + -2x2 Reorder the terms: 72 + 36x + -2x2 = -72 + 72 + -36x + 36x + 2x2 + -2x2 Combine like terms: -72 + 72 = 0 72 + 36x + -2x2 = 0 + -36x + 36x + 2x2 + -2x2 72 + 36x + -2x2 = -36x + 36x + 2x2 + -2x2 Combine like terms: -36x + 36x = 0 72 + 36x + -2x2 = 0 + 2x2 + -2x2 72 + 36x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 72 + 36x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 18x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 18x + -1x2)' equal to zero and attempt to solve: Simplifying 36 + 18x + -1x2 = 0 Solving 36 + 18x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -18x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -18x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -18x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -18x + x2 = 0 + 36 -18x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -18x + x2 = 36 The x term is -18x. Take half its coefficient (-9). Square it (81) and add it to both sides. Add '81' to each side of the equation. -18x + 81 + x2 = 36 + 81 Reorder the terms: 81 + -18x + x2 = 36 + 81 Combine like terms: 36 + 81 = 117 81 + -18x + x2 = 117 Factor a perfect square on the left side: (x + -9)(x + -9) = 117 Calculate the square root of the right side: 10.816653826 Break this problem into two subproblems by setting (x + -9) equal to 10.816653826 and -10.816653826.Subproblem 1
x + -9 = 10.816653826 Simplifying x + -9 = 10.816653826 Reorder the terms: -9 + x = 10.816653826 Solving -9 + x = 10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + x = 10.816653826 + 9 x = 10.816653826 + 9 Combine like terms: 10.816653826 + 9 = 19.816653826 x = 19.816653826 Simplifying x = 19.816653826Subproblem 2
x + -9 = -10.816653826 Simplifying x + -9 = -10.816653826 Reorder the terms: -9 + x = -10.816653826 Solving -9 + x = -10.816653826 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = -10.816653826 + 9 Combine like terms: -9 + 9 = 0 0 + x = -10.816653826 + 9 x = -10.816653826 + 9 Combine like terms: -10.816653826 + 9 = -1.816653826 x = -1.816653826 Simplifying x = -1.816653826Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.816653826, -1.816653826}Solution
x = {19.816653826, -1.816653826}
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