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Simplifying x2 + 31x + 72 = 0 Reorder the terms: 72 + 31x + x2 = 0 Solving 72 + 31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + 31x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + 31x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + 31x + x2 = 0 + -72 31x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 31x + x2 = -72 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = -72 + 240.25 Reorder the terms: 240.25 + 31x + x2 = -72 + 240.25 Combine like terms: -72 + 240.25 = 168.25 240.25 + 31x + x2 = 168.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 168.25 Calculate the square root of the right side: 12.971121771 Break this problem into two subproblems by setting (x + 15.5) equal to 12.971121771 and -12.971121771.Subproblem 1
x + 15.5 = 12.971121771 Simplifying x + 15.5 = 12.971121771 Reorder the terms: 15.5 + x = 12.971121771 Solving 15.5 + x = 12.971121771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 12.971121771 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 12.971121771 + -15.5 x = 12.971121771 + -15.5 Combine like terms: 12.971121771 + -15.5 = -2.528878229 x = -2.528878229 Simplifying x = -2.528878229Subproblem 2
x + 15.5 = -12.971121771 Simplifying x + 15.5 = -12.971121771 Reorder the terms: 15.5 + x = -12.971121771 Solving 15.5 + x = -12.971121771 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -12.971121771 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -12.971121771 + -15.5 x = -12.971121771 + -15.5 Combine like terms: -12.971121771 + -15.5 = -28.471121771 x = -28.471121771 Simplifying x = -28.471121771Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.528878229, -28.471121771}
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