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Simplifying 24x2 + 3x + -50 = 0 Reorder the terms: -50 + 3x + 24x2 = 0 Solving -50 + 3x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -2.083333333 + 0.125x + x2 = 0 Move the constant term to the right: Add '2.083333333' to each side of the equation. -2.083333333 + 0.125x + 2.083333333 + x2 = 0 + 2.083333333 Reorder the terms: -2.083333333 + 2.083333333 + 0.125x + x2 = 0 + 2.083333333 Combine like terms: -2.083333333 + 2.083333333 = 0.000000000 0.000000000 + 0.125x + x2 = 0 + 2.083333333 0.125x + x2 = 0 + 2.083333333 Combine like terms: 0 + 2.083333333 = 2.083333333 0.125x + x2 = 2.083333333 The x term is 0.125x. Take half its coefficient (0.0625). Square it (0.00390625) and add it to both sides. Add '0.00390625' to each side of the equation. 0.125x + 0.00390625 + x2 = 2.083333333 + 0.00390625 Reorder the terms: 0.00390625 + 0.125x + x2 = 2.083333333 + 0.00390625 Combine like terms: 2.083333333 + 0.00390625 = 2.087239583 0.00390625 + 0.125x + x2 = 2.087239583 Factor a perfect square on the left side: (x + 0.0625)(x + 0.0625) = 2.087239583 Calculate the square root of the right side: 1.444728204 Break this problem into two subproblems by setting (x + 0.0625) equal to 1.444728204 and -1.444728204.Subproblem 1
x + 0.0625 = 1.444728204 Simplifying x + 0.0625 = 1.444728204 Reorder the terms: 0.0625 + x = 1.444728204 Solving 0.0625 + x = 1.444728204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 1.444728204 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 1.444728204 + -0.0625 x = 1.444728204 + -0.0625 Combine like terms: 1.444728204 + -0.0625 = 1.382228204 x = 1.382228204 Simplifying x = 1.382228204Subproblem 2
x + 0.0625 = -1.444728204 Simplifying x + 0.0625 = -1.444728204 Reorder the terms: 0.0625 + x = -1.444728204 Solving 0.0625 + x = -1.444728204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -1.444728204 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -1.444728204 + -0.0625 x = -1.444728204 + -0.0625 Combine like terms: -1.444728204 + -0.0625 = -1.507228204 x = -1.507228204 Simplifying x = -1.507228204Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.382228204, -1.507228204}
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