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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 = 28.471121771 x = 28.471121771 Simplifying x = 28.471121771Subproblem 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 = 2.528878229 x = 2.528878229 Simplifying x = 2.528878229Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.471121771, 2.528878229}
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