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Simplifying -2x2 + 26x + 72 = 0 Reorder the terms: 72 + 26x + -2x2 = 0 Solving 72 + 26x + -2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(36 + 13x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(36 + 13x + -1x2)' equal to zero and attempt to solve: Simplifying 36 + 13x + -1x2 = 0 Solving 36 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + -13x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + -13x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + -13x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + -13x + x2 = 0 + 36 -13x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 -13x + x2 = 36 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 36 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 36 + 42.25 Combine like terms: 36 + 42.25 = 78.25 42.25 + -13x + x2 = 78.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + -6.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + -6.5 = 8.845903006 Simplifying x + -6.5 = 8.845903006 Reorder the terms: -6.5 + x = 8.845903006 Solving -6.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.845903006 + 6.5 x = 8.845903006 + 6.5 Combine like terms: 8.845903006 + 6.5 = 15.345903006 x = 15.345903006 Simplifying x = 15.345903006Subproblem 2
x + -6.5 = -8.845903006 Simplifying x + -6.5 = -8.845903006 Reorder the terms: -6.5 + x = -8.845903006 Solving -6.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.845903006 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.845903006 + 6.5 x = -8.845903006 + 6.5 Combine like terms: -8.845903006 + 6.5 = -2.345903006 x = -2.345903006 Simplifying x = -2.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.345903006, -2.345903006}Solution
x = {15.345903006, -2.345903006}
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