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Simplifying 4x + 5 = x2 + 5x + -24 Reorder the terms: 5 + 4x = x2 + 5x + -24 Reorder the terms: 5 + 4x = -24 + 5x + x2 Solving 5 + 4x = -24 + 5x + x2 Solving for variable 'x'. Reorder the terms: 5 + 24 + 4x + -5x + -1x2 = -24 + 5x + x2 + 24 + -5x + -1x2 Combine like terms: 5 + 24 = 29 29 + 4x + -5x + -1x2 = -24 + 5x + x2 + 24 + -5x + -1x2 Combine like terms: 4x + -5x = -1x 29 + -1x + -1x2 = -24 + 5x + x2 + 24 + -5x + -1x2 Reorder the terms: 29 + -1x + -1x2 = -24 + 24 + 5x + -5x + x2 + -1x2 Combine like terms: -24 + 24 = 0 29 + -1x + -1x2 = 0 + 5x + -5x + x2 + -1x2 29 + -1x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 29 + -1x + -1x2 = 0 + x2 + -1x2 29 + -1x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 29 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -29 + x + x2 = 0 Move the constant term to the right: Add '29' to each side of the equation. -29 + x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + x + x2 = 0 + 29 x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 x + x2 = 29 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 29 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 29 + 0.25 Combine like terms: 29 + 0.25 = 29.25 1.25 + x2 = 29.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 29.25 Calculate the square root of the right side: 5.408326913 Break this problem into two subproblems by setting (x + 0.5) equal to 5.408326913 and -5.408326913.Subproblem 1
x + 0.5 = 5.408326913 Simplifying x + 0.5 = 5.408326913 Reorder the terms: 0.5 + x = 5.408326913 Solving 0.5 + x = 5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 5.408326913 + -0.5 x = 5.408326913 + -0.5 Combine like terms: 5.408326913 + -0.5 = 4.908326913 x = 4.908326913 Simplifying x = 4.908326913Subproblem 2
x + 0.5 = -5.408326913 Simplifying x + 0.5 = -5.408326913 Reorder the terms: 0.5 + x = -5.408326913 Solving 0.5 + x = -5.408326913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -5.408326913 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -5.408326913 + -0.5 x = -5.408326913 + -0.5 Combine like terms: -5.408326913 + -0.5 = -5.908326913 x = -5.908326913 Simplifying x = -5.908326913Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.908326913, -5.908326913}
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