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Simplifying x2 + 24x + -84 = 29 Reorder the terms: -84 + 24x + x2 = 29 Solving -84 + 24x + x2 = 29 Solving for variable 'x'. Reorder the terms: -84 + -29 + 24x + x2 = 29 + -29 Combine like terms: -84 + -29 = -113 -113 + 24x + x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -113 + 24x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + 24x + 113 + x2 = 0 + 113 Reorder the terms: -113 + 113 + 24x + x2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + 24x + x2 = 0 + 113 24x + x2 = 0 + 113 Combine like terms: 0 + 113 = 113 24x + x2 = 113 The x term is 24x. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24x + 144 + x2 = 113 + 144 Reorder the terms: 144 + 24x + x2 = 113 + 144 Combine like terms: 113 + 144 = 257 144 + 24x + x2 = 257 Factor a perfect square on the left side: (x + 12)(x + 12) = 257 Calculate the square root of the right side: 16.031219542 Break this problem into two subproblems by setting (x + 12) equal to 16.031219542 and -16.031219542.Subproblem 1
x + 12 = 16.031219542 Simplifying x + 12 = 16.031219542 Reorder the terms: 12 + x = 16.031219542 Solving 12 + x = 16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 16.031219542 + -12 Combine like terms: 12 + -12 = 0 0 + x = 16.031219542 + -12 x = 16.031219542 + -12 Combine like terms: 16.031219542 + -12 = 4.031219542 x = 4.031219542 Simplifying x = 4.031219542Subproblem 2
x + 12 = -16.031219542 Simplifying x + 12 = -16.031219542 Reorder the terms: 12 + x = -16.031219542 Solving 12 + x = -16.031219542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = -16.031219542 + -12 Combine like terms: 12 + -12 = 0 0 + x = -16.031219542 + -12 x = -16.031219542 + -12 Combine like terms: -16.031219542 + -12 = -28.031219542 x = -28.031219542 Simplifying x = -28.031219542Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.031219542, -28.031219542}
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