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Simplifying 24x2 + 25x + -144 = 0 Reorder the terms: -144 + 25x + 24x2 = 0 Solving -144 + 25x + 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'. -6 + 1.041666667x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.041666667x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.041666667x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.041666667x + x2 = 0 + 6 1.041666667x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.041666667x + x2 = 6 The x term is 1.041666667x. Take half its coefficient (0.5208333335). Square it (0.2712673613) and add it to both sides. Add '0.2712673613' to each side of the equation. 1.041666667x + 0.2712673613 + x2 = 6 + 0.2712673613 Reorder the terms: 0.2712673613 + 1.041666667x + x2 = 6 + 0.2712673613 Combine like terms: 6 + 0.2712673613 = 6.2712673613 0.2712673613 + 1.041666667x + x2 = 6.2712673613 Factor a perfect square on the left side: (x + 0.5208333335)(x + 0.5208333335) = 6.2712673613 Calculate the square root of the right side: 2.50424986 Break this problem into two subproblems by setting (x + 0.5208333335) equal to 2.50424986 and -2.50424986.Subproblem 1
x + 0.5208333335 = 2.50424986 Simplifying x + 0.5208333335 = 2.50424986 Reorder the terms: 0.5208333335 + x = 2.50424986 Solving 0.5208333335 + x = 2.50424986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = 2.50424986 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = 2.50424986 + -0.5208333335 x = 2.50424986 + -0.5208333335 Combine like terms: 2.50424986 + -0.5208333335 = 1.9834165265 x = 1.9834165265 Simplifying x = 1.9834165265Subproblem 2
x + 0.5208333335 = -2.50424986 Simplifying x + 0.5208333335 = -2.50424986 Reorder the terms: 0.5208333335 + x = -2.50424986 Solving 0.5208333335 + x = -2.50424986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5208333335' to each side of the equation. 0.5208333335 + -0.5208333335 + x = -2.50424986 + -0.5208333335 Combine like terms: 0.5208333335 + -0.5208333335 = 0.0000000000 0.0000000000 + x = -2.50424986 + -0.5208333335 x = -2.50424986 + -0.5208333335 Combine like terms: -2.50424986 + -0.5208333335 = -3.0250831935 x = -3.0250831935 Simplifying x = -3.0250831935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.9834165265, -3.0250831935}
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