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Simplifying 2x2 + 31x + -91 = 0 Reorder the terms: -91 + 31x + 2x2 = 0 Solving -91 + 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'. -45.5 + 15.5x + x2 = 0 Move the constant term to the right: Add '45.5' to each side of the equation. -45.5 + 15.5x + 45.5 + x2 = 0 + 45.5 Reorder the terms: -45.5 + 45.5 + 15.5x + x2 = 0 + 45.5 Combine like terms: -45.5 + 45.5 = 0.0 0.0 + 15.5x + x2 = 0 + 45.5 15.5x + x2 = 0 + 45.5 Combine like terms: 0 + 45.5 = 45.5 15.5x + x2 = 45.5 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 = 45.5 + 60.0625 Reorder the terms: 60.0625 + 15.5x + x2 = 45.5 + 60.0625 Combine like terms: 45.5 + 60.0625 = 105.5625 60.0625 + 15.5x + x2 = 105.5625 Factor a perfect square on the left side: (x + 7.75)(x + 7.75) = 105.5625 Calculate the square root of the right side: 10.274361294 Break this problem into two subproblems by setting (x + 7.75) equal to 10.274361294 and -10.274361294.Subproblem 1
x + 7.75 = 10.274361294 Simplifying x + 7.75 = 10.274361294 Reorder the terms: 7.75 + x = 10.274361294 Solving 7.75 + x = 10.274361294 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 = 10.274361294 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = 10.274361294 + -7.75 x = 10.274361294 + -7.75 Combine like terms: 10.274361294 + -7.75 = 2.524361294 x = 2.524361294 Simplifying x = 2.524361294Subproblem 2
x + 7.75 = -10.274361294 Simplifying x + 7.75 = -10.274361294 Reorder the terms: 7.75 + x = -10.274361294 Solving 7.75 + x = -10.274361294 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 = -10.274361294 + -7.75 Combine like terms: 7.75 + -7.75 = 0.00 0.00 + x = -10.274361294 + -7.75 x = -10.274361294 + -7.75 Combine like terms: -10.274361294 + -7.75 = -18.024361294 x = -18.024361294 Simplifying x = -18.024361294Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.524361294, -18.024361294}
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