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Simplifying 2x2 + -31x + -280 = 0 Reorder the terms: -280 + -31x + 2x2 = 0 Solving -280 + -31x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -140 + -15.5x + x2 = 0 Move the constant term to the right: Add '140' to each side of the equation. -140 + -15.5x + 140 + x2 = 0 + 140 Reorder the terms: -140 + 140 + -15.5x + x2 = 0 + 140 Combine like terms: -140 + 140 = 0 0 + -15.5x + x2 = 0 + 140 -15.5x + x2 = 0 + 140 Combine like terms: 0 + 140 = 140 -15.5x + x2 = 140 The x term is -15.5x. Take half its coefficient (-7.75). Square it (60.0625) and add it to both sides. Add '60.0625' to each side of the equation. -15.5x + 60.0625 + x2 = 140 + 60.0625 Reorder the terms: 60.0625 + -15.5x + x2 = 140 + 60.0625 Combine like terms: 140 + 60.0625 = 200.0625 60.0625 + -15.5x + x2 = 200.0625 Factor a perfect square on the left side: (x + -7.75)(x + -7.75) = 200.0625 Calculate the square root of the right side: 14.14434516 Break this problem into two subproblems by setting (x + -7.75) equal to 14.14434516 and -14.14434516.Subproblem 1
x + -7.75 = 14.14434516 Simplifying x + -7.75 = 14.14434516 Reorder the terms: -7.75 + x = 14.14434516 Solving -7.75 + x = 14.14434516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = 14.14434516 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = 14.14434516 + 7.75 x = 14.14434516 + 7.75 Combine like terms: 14.14434516 + 7.75 = 21.89434516 x = 21.89434516 Simplifying x = 21.89434516Subproblem 2
x + -7.75 = -14.14434516 Simplifying x + -7.75 = -14.14434516 Reorder the terms: -7.75 + x = -14.14434516 Solving -7.75 + x = -14.14434516 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.75' to each side of the equation. -7.75 + 7.75 + x = -14.14434516 + 7.75 Combine like terms: -7.75 + 7.75 = 0.00 0.00 + x = -14.14434516 + 7.75 x = -14.14434516 + 7.75 Combine like terms: -14.14434516 + 7.75 = -6.39434516 x = -6.39434516 Simplifying x = -6.39434516Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.89434516, -6.39434516}
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