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Simplifying x2 + -31x + -8 = 0 Reorder the terms: -8 + -31x + x2 = 0 Solving -8 + -31x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -31x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -31x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -31x + x2 = 0 + 8 -31x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -31x + x2 = 8 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 = 8 + 240.25 Reorder the terms: 240.25 + -31x + x2 = 8 + 240.25 Combine like terms: 8 + 240.25 = 248.25 240.25 + -31x + x2 = 248.25 Factor a perfect square on the left side: (x + -15.5)(x + -15.5) = 248.25 Calculate the square root of the right side: 15.755951257 Break this problem into two subproblems by setting (x + -15.5) equal to 15.755951257 and -15.755951257.Subproblem 1
x + -15.5 = 15.755951257 Simplifying x + -15.5 = 15.755951257 Reorder the terms: -15.5 + x = 15.755951257 Solving -15.5 + x = 15.755951257 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 = 15.755951257 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = 15.755951257 + 15.5 x = 15.755951257 + 15.5 Combine like terms: 15.755951257 + 15.5 = 31.255951257 x = 31.255951257 Simplifying x = 31.255951257Subproblem 2
x + -15.5 = -15.755951257 Simplifying x + -15.5 = -15.755951257 Reorder the terms: -15.5 + x = -15.755951257 Solving -15.5 + x = -15.755951257 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 = -15.755951257 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + x = -15.755951257 + 15.5 x = -15.755951257 + 15.5 Combine like terms: -15.755951257 + 15.5 = -0.255951257 x = -0.255951257 Simplifying x = -0.255951257Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.255951257, -0.255951257}
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