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Simplifying 4x2 + -31x + -257 = 0 Reorder the terms: -257 + -31x + 4x2 = 0 Solving -257 + -31x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -64.25 + -7.75x + x2 = 0 Move the constant term to the right: Add '64.25' to each side of the equation. -64.25 + -7.75x + 64.25 + x2 = 0 + 64.25 Reorder the terms: -64.25 + 64.25 + -7.75x + x2 = 0 + 64.25 Combine like terms: -64.25 + 64.25 = 0.00 0.00 + -7.75x + x2 = 0 + 64.25 -7.75x + x2 = 0 + 64.25 Combine like terms: 0 + 64.25 = 64.25 -7.75x + x2 = 64.25 The x term is -7.75x. Take half its coefficient (-3.875). Square it (15.015625) and add it to both sides. Add '15.015625' to each side of the equation. -7.75x + 15.015625 + x2 = 64.25 + 15.015625 Reorder the terms: 15.015625 + -7.75x + x2 = 64.25 + 15.015625 Combine like terms: 64.25 + 15.015625 = 79.265625 15.015625 + -7.75x + x2 = 79.265625 Factor a perfect square on the left side: (x + -3.875)(x + -3.875) = 79.265625 Calculate the square root of the right side: 8.903124452 Break this problem into two subproblems by setting (x + -3.875) equal to 8.903124452 and -8.903124452.Subproblem 1
x + -3.875 = 8.903124452 Simplifying x + -3.875 = 8.903124452 Reorder the terms: -3.875 + x = 8.903124452 Solving -3.875 + x = 8.903124452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = 8.903124452 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = 8.903124452 + 3.875 x = 8.903124452 + 3.875 Combine like terms: 8.903124452 + 3.875 = 12.778124452 x = 12.778124452 Simplifying x = 12.778124452Subproblem 2
x + -3.875 = -8.903124452 Simplifying x + -3.875 = -8.903124452 Reorder the terms: -3.875 + x = -8.903124452 Solving -3.875 + x = -8.903124452 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.875' to each side of the equation. -3.875 + 3.875 + x = -8.903124452 + 3.875 Combine like terms: -3.875 + 3.875 = 0.000 0.000 + x = -8.903124452 + 3.875 x = -8.903124452 + 3.875 Combine like terms: -8.903124452 + 3.875 = -5.028124452 x = -5.028124452 Simplifying x = -5.028124452Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.778124452, -5.028124452}
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