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Simplifying x2 + 8x + -7 = -9x + 5 Reorder the terms: -7 + 8x + x2 = -9x + 5 Reorder the terms: -7 + 8x + x2 = 5 + -9x Solving -7 + 8x + x2 = 5 + -9x Solving for variable 'x'. Reorder the terms: -7 + -5 + 8x + 9x + x2 = 5 + -9x + -5 + 9x Combine like terms: -7 + -5 = -12 -12 + 8x + 9x + x2 = 5 + -9x + -5 + 9x Combine like terms: 8x + 9x = 17x -12 + 17x + x2 = 5 + -9x + -5 + 9x Reorder the terms: -12 + 17x + x2 = 5 + -5 + -9x + 9x Combine like terms: 5 + -5 = 0 -12 + 17x + x2 = 0 + -9x + 9x -12 + 17x + x2 = -9x + 9x Combine like terms: -9x + 9x = 0 -12 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 17x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 17x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 17x + x2 = 0 + 12 17x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 17x + x2 = 12 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 12 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 12 + 72.25 Combine like terms: 12 + 72.25 = 84.25 72.25 + 17x + x2 = 84.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 84.25 Calculate the square root of the right side: 9.178779875 Break this problem into two subproblems by setting (x + 8.5) equal to 9.178779875 and -9.178779875.Subproblem 1
x + 8.5 = 9.178779875 Simplifying x + 8.5 = 9.178779875 Reorder the terms: 8.5 + x = 9.178779875 Solving 8.5 + x = 9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 9.178779875 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 9.178779875 + -8.5 x = 9.178779875 + -8.5 Combine like terms: 9.178779875 + -8.5 = 0.678779875 x = 0.678779875 Simplifying x = 0.678779875Subproblem 2
x + 8.5 = -9.178779875 Simplifying x + 8.5 = -9.178779875 Reorder the terms: 8.5 + x = -9.178779875 Solving 8.5 + x = -9.178779875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -9.178779875 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -9.178779875 + -8.5 x = -9.178779875 + -8.5 Combine like terms: -9.178779875 + -8.5 = -17.678779875 x = -17.678779875 Simplifying x = -17.678779875Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.678779875, -17.678779875}
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