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Simplifying 9(x + x2) = 99 (x * 9 + x2 * 9) = 99 (9x + 9x2) = 99 Solving 9x + 9x2 = 99 Solving for variable 'x'. Reorder the terms: -99 + 9x + 9x2 = 99 + -99 Combine like terms: 99 + -99 = 0 -99 + 9x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '9'. 9(-11 + x + x2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(-11 + x + x2)' equal to zero and attempt to solve: Simplifying -11 + x + x2 = 0 Solving -11 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + x + x2 = 0 + 11 x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 x + x2 = 11 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. x + 0.25 + x2 = 11 + 0.25 Reorder the terms: 0.25 + x + x2 = 11 + 0.25 Combine like terms: 11 + 0.25 = 11.25 0.25 + x + x2 = 11.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 11.25 Calculate the square root of the right side: 3.354101966 Break this problem into two subproblems by setting (x + 0.5) equal to 3.354101966 and -3.354101966.Subproblem 1
x + 0.5 = 3.354101966 Simplifying x + 0.5 = 3.354101966 Reorder the terms: 0.5 + x = 3.354101966 Solving 0.5 + x = 3.354101966 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 = 3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.354101966 + -0.5 x = 3.354101966 + -0.5 Combine like terms: 3.354101966 + -0.5 = 2.854101966 x = 2.854101966 Simplifying x = 2.854101966Subproblem 2
x + 0.5 = -3.354101966 Simplifying x + 0.5 = -3.354101966 Reorder the terms: 0.5 + x = -3.354101966 Solving 0.5 + x = -3.354101966 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 = -3.354101966 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.354101966 + -0.5 x = -3.354101966 + -0.5 Combine like terms: -3.354101966 + -0.5 = -3.854101966 x = -3.854101966 Simplifying x = -3.854101966Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.854101966, -3.854101966}Solution
x = {2.854101966, -3.854101966}
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