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Simplifying 0 = 3x2 + -72x + -537 Reorder the terms: 0 = -537 + -72x + 3x2 Solving 0 = -537 + -72x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 537 = 537 537 + 72x + -3x2 = -537 + -72x + 3x2 + 537 + 72x + -3x2 Reorder the terms: 537 + 72x + -3x2 = -537 + 537 + -72x + 72x + 3x2 + -3x2 Combine like terms: -537 + 537 = 0 537 + 72x + -3x2 = 0 + -72x + 72x + 3x2 + -3x2 537 + 72x + -3x2 = -72x + 72x + 3x2 + -3x2 Combine like terms: -72x + 72x = 0 537 + 72x + -3x2 = 0 + 3x2 + -3x2 537 + 72x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 537 + 72x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(179 + 24x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(179 + 24x + -1x2)' equal to zero and attempt to solve: Simplifying 179 + 24x + -1x2 = 0 Solving 179 + 24x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -179 + -24x + x2 = 0 Move the constant term to the right: Add '179' to each side of the equation. -179 + -24x + 179 + x2 = 0 + 179 Reorder the terms: -179 + 179 + -24x + x2 = 0 + 179 Combine like terms: -179 + 179 = 0 0 + -24x + x2 = 0 + 179 -24x + x2 = 0 + 179 Combine like terms: 0 + 179 = 179 -24x + x2 = 179 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = 179 + 144 Reorder the terms: 144 + -24x + x2 = 179 + 144 Combine like terms: 179 + 144 = 323 144 + -24x + x2 = 323 Factor a perfect square on the left side: (x + -12)(x + -12) = 323 Calculate the square root of the right side: 17.972200756 Break this problem into two subproblems by setting (x + -12) equal to 17.972200756 and -17.972200756.Subproblem 1
x + -12 = 17.972200756 Simplifying x + -12 = 17.972200756 Reorder the terms: -12 + x = 17.972200756 Solving -12 + x = 17.972200756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 17.972200756 + 12 Combine like terms: -12 + 12 = 0 0 + x = 17.972200756 + 12 x = 17.972200756 + 12 Combine like terms: 17.972200756 + 12 = 29.972200756 x = 29.972200756 Simplifying x = 29.972200756Subproblem 2
x + -12 = -17.972200756 Simplifying x + -12 = -17.972200756 Reorder the terms: -12 + x = -17.972200756 Solving -12 + x = -17.972200756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -17.972200756 + 12 Combine like terms: -12 + 12 = 0 0 + x = -17.972200756 + 12 x = -17.972200756 + 12 Combine like terms: -17.972200756 + 12 = -5.972200756 x = -5.972200756 Simplifying x = -5.972200756Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.972200756, -5.972200756}Solution
x = {29.972200756, -5.972200756}
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