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Simplifying x2 + 9x = 88 Reorder the terms: 9x + x2 = 88 Solving 9x + x2 = 88 Solving for variable 'x'. Reorder the terms: -88 + 9x + x2 = 88 + -88 Combine like terms: 88 + -88 = 0 -88 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '88' to each side of the equation. -88 + 9x + 88 + x2 = 0 + 88 Reorder the terms: -88 + 88 + 9x + x2 = 0 + 88 Combine like terms: -88 + 88 = 0 0 + 9x + x2 = 0 + 88 9x + x2 = 0 + 88 Combine like terms: 0 + 88 = 88 9x + x2 = 88 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 88 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 88 + 20.25 Combine like terms: 88 + 20.25 = 108.25 20.25 + 9x + x2 = 108.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + 4.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + 4.5 = 10.404326023 Simplifying x + 4.5 = 10.404326023 Reorder the terms: 4.5 + x = 10.404326023 Solving 4.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 10.404326023 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.404326023 + -4.5 x = 10.404326023 + -4.5 Combine like terms: 10.404326023 + -4.5 = 5.904326023 x = 5.904326023 Simplifying x = 5.904326023Subproblem 2
x + 4.5 = -10.404326023 Simplifying x + 4.5 = -10.404326023 Reorder the terms: 4.5 + x = -10.404326023 Solving 4.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -10.404326023 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.404326023 + -4.5 x = -10.404326023 + -4.5 Combine like terms: -10.404326023 + -4.5 = -14.904326023 x = -14.904326023 Simplifying x = -14.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.904326023, -14.904326023}
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