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Simplifying x2 + -31x + 41 = 0 Reorder the terms: 41 + -31x + x2 = 0 Solving 41 + -31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-41' to each side of the equation. 41 + -31x + -41 + x2 = 0 + -41 Reorder the terms: 41 + -41 + -31x + x2 = 0 + -41 Combine like terms: 41 + -41 = 0 0 + -31x + x2 = 0 + -41 -31x + x2 = 0 + -41 Combine like terms: 0 + -41 = -41 -31x + x2 = -41 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 = -41 + 240.25 Reorder the terms: 240.25 + -31x + x2 = -41 + 240.25 Combine like terms: -41 + 240.25 = 199.25 240.25 + -31x + x2 = 199.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 199.25 Calculate the square root of the right side: 14.115594213 Break this problem into two subproblems by setting (x + -15.5) equal to 14.115594213 and -14.115594213.Subproblem 1
x + -15.5 = 14.115594213 Simplifying x + -15.5 = 14.115594213 Reorder the terms: -15.5 + x = 14.115594213 Solving -15.5 + x = 14.115594213 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 = 14.115594213 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 14.115594213 + 15.5 x = 14.115594213 + 15.5 Combine like terms: 14.115594213 + 15.5 = 29.615594213 x = 29.615594213 Simplifying x = 29.615594213Subproblem 2
x + -15.5 = -14.115594213 Simplifying x + -15.5 = -14.115594213 Reorder the terms: -15.5 + x = -14.115594213 Solving -15.5 + x = -14.115594213 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 = -14.115594213 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -14.115594213 + 15.5 x = -14.115594213 + 15.5 Combine like terms: -14.115594213 + 15.5 = 1.384405787 x = 1.384405787 Simplifying x = 1.384405787Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.615594213, 1.384405787}
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