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Simplifying 4x2 + -68x + -31x + -289 = 0 Reorder the terms: -289 + -68x + -31x + 4x2 = 0 Combine like terms: -68x + -31x = -99x -289 + -99x + 4x2 = 0 Solving -289 + -99x + 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'. -72.25 + -24.75x + x2 = 0 Move the constant term to the right: Add '72.25' to each side of the equation. -72.25 + -24.75x + 72.25 + x2 = 0 + 72.25 Reorder the terms: -72.25 + 72.25 + -24.75x + x2 = 0 + 72.25 Combine like terms: -72.25 + 72.25 = 0.00 0.00 + -24.75x + x2 = 0 + 72.25 -24.75x + x2 = 0 + 72.25 Combine like terms: 0 + 72.25 = 72.25 -24.75x + x2 = 72.25 The x term is -24.75x. Take half its coefficient (-12.375). Square it (153.140625) and add it to both sides. Add '153.140625' to each side of the equation. -24.75x + 153.140625 + x2 = 72.25 + 153.140625 Reorder the terms: 153.140625 + -24.75x + x2 = 72.25 + 153.140625 Combine like terms: 72.25 + 153.140625 = 225.390625 153.140625 + -24.75x + x2 = 225.390625 Factor a perfect square on the left side: (x + -12.375)(x + -12.375) = 225.390625 Calculate the square root of the right side: 15.013015187 Break this problem into two subproblems by setting (x + -12.375) equal to 15.013015187 and -15.013015187.Subproblem 1
x + -12.375 = 15.013015187 Simplifying x + -12.375 = 15.013015187 Reorder the terms: -12.375 + x = 15.013015187 Solving -12.375 + x = 15.013015187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.375' to each side of the equation. -12.375 + 12.375 + x = 15.013015187 + 12.375 Combine like terms: -12.375 + 12.375 = 0.000 0.000 + x = 15.013015187 + 12.375 x = 15.013015187 + 12.375 Combine like terms: 15.013015187 + 12.375 = 27.388015187 x = 27.388015187 Simplifying x = 27.388015187Subproblem 2
x + -12.375 = -15.013015187 Simplifying x + -12.375 = -15.013015187 Reorder the terms: -12.375 + x = -15.013015187 Solving -12.375 + x = -15.013015187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.375' to each side of the equation. -12.375 + 12.375 + x = -15.013015187 + 12.375 Combine like terms: -12.375 + 12.375 = 0.000 0.000 + x = -15.013015187 + 12.375 x = -15.013015187 + 12.375 Combine like terms: -15.013015187 + 12.375 = -2.638015187 x = -2.638015187 Simplifying x = -2.638015187Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.388015187, -2.638015187}
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