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Simplifying 4x2 + 129x + -360 = 0 Reorder the terms: -360 + 129x + 4x2 = 0 Solving -360 + 129x + 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'. -90 + 32.25x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + 32.25x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + 32.25x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 32.25x + x2 = 0 + 90 32.25x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 32.25x + x2 = 90 The x term is 32.25x. Take half its coefficient (16.125). Square it (260.015625) and add it to both sides. Add '260.015625' to each side of the equation. 32.25x + 260.015625 + x2 = 90 + 260.015625 Reorder the terms: 260.015625 + 32.25x + x2 = 90 + 260.015625 Combine like terms: 90 + 260.015625 = 350.015625 260.015625 + 32.25x + x2 = 350.015625 Factor a perfect square on the left side: (x + 16.125)(x + 16.125) = 350.015625 Calculate the square root of the right side: 18.708704525 Break this problem into two subproblems by setting (x + 16.125) equal to 18.708704525 and -18.708704525.Subproblem 1
x + 16.125 = 18.708704525 Simplifying x + 16.125 = 18.708704525 Reorder the terms: 16.125 + x = 18.708704525 Solving 16.125 + x = 18.708704525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.125' to each side of the equation. 16.125 + -16.125 + x = 18.708704525 + -16.125 Combine like terms: 16.125 + -16.125 = 0.000 0.000 + x = 18.708704525 + -16.125 x = 18.708704525 + -16.125 Combine like terms: 18.708704525 + -16.125 = 2.583704525 x = 2.583704525 Simplifying x = 2.583704525Subproblem 2
x + 16.125 = -18.708704525 Simplifying x + 16.125 = -18.708704525 Reorder the terms: 16.125 + x = -18.708704525 Solving 16.125 + x = -18.708704525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.125' to each side of the equation. 16.125 + -16.125 + x = -18.708704525 + -16.125 Combine like terms: 16.125 + -16.125 = 0.000 0.000 + x = -18.708704525 + -16.125 x = -18.708704525 + -16.125 Combine like terms: -18.708704525 + -16.125 = -34.833704525 x = -34.833704525 Simplifying x = -34.833704525Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.583704525, -34.833704525}
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