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Simplifying -9 = 8x + x2 Solving -9 = 8x + x2 Solving for variable 'x'. Reorder the terms: -9 + -8x + -1x2 = 8x + -8x + x2 + -1x2 Combine like terms: 8x + -8x = 0 -9 + -8x + -1x2 = 0 + x2 + -1x2 -9 + -8x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + -8x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 8x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 8x + x2)' equal to zero and attempt to solve: Simplifying 9 + 8x + x2 = 0 Solving 9 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 8x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 8x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 8x + x2 = 0 + -9 8x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 8x + x2 = -9 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = -9 + 16 Reorder the terms: 16 + 8x + x2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + 8x + x2 = 7 Factor a perfect square on the left side: (x + 4)(x + 4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 4) equal to 2.645751311 and -2.645751311.Subproblem 1
x + 4 = 2.645751311 Simplifying x + 4 = 2.645751311 Reorder the terms: 4 + x = 2.645751311 Solving 4 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = 2.645751311 + -4 x = 2.645751311 + -4 Combine like terms: 2.645751311 + -4 = -1.354248689 x = -1.354248689 Simplifying x = -1.354248689Subproblem 2
x + 4 = -2.645751311 Simplifying x + 4 = -2.645751311 Reorder the terms: 4 + x = -2.645751311 Solving 4 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -2.645751311 + -4 Combine like terms: 4 + -4 = 0 0 + x = -2.645751311 + -4 x = -2.645751311 + -4 Combine like terms: -2.645751311 + -4 = -6.645751311 x = -6.645751311 Simplifying x = -6.645751311Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.354248689, -6.645751311}Solution
x = {-1.354248689, -6.645751311}
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