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Simplifying 18 = 6x + x(x + 13) Reorder the terms: 18 = 6x + x(13 + x) 18 = 6x + (13 * x + x * x) 18 = 6x + (13x + x2) Combine like terms: 6x + 13x = 19x 18 = 19x + x2 Solving 18 = 19x + x2 Solving for variable 'x'. Reorder the terms: 18 + -19x + -1x2 = 19x + -19x + x2 + -1x2 Combine like terms: 19x + -19x = 0 18 + -19x + -1x2 = 0 + x2 + -1x2 18 + -19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 18 + -19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -18 + 19x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 19x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 19x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 19x + x2 = 0 + 18 19x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 19x + x2 = 18 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = 18 + 90.25 Reorder the terms: 90.25 + 19x + x2 = 18 + 90.25 Combine like terms: 18 + 90.25 = 108.25 90.25 + 19x + x2 = 108.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + 9.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + 9.5 = 10.404326023 Simplifying x + 9.5 = 10.404326023 Reorder the terms: 9.5 + x = 10.404326023 Solving 9.5 + x = 10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 10.404326023 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 10.404326023 + -9.5 x = 10.404326023 + -9.5 Combine like terms: 10.404326023 + -9.5 = 0.904326023 x = 0.904326023 Simplifying x = 0.904326023Subproblem 2
x + 9.5 = -10.404326023 Simplifying x + 9.5 = -10.404326023 Reorder the terms: 9.5 + x = -10.404326023 Solving 9.5 + x = -10.404326023 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -10.404326023 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -10.404326023 + -9.5 x = -10.404326023 + -9.5 Combine like terms: -10.404326023 + -9.5 = -19.904326023 x = -19.904326023 Simplifying x = -19.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.904326023, -19.904326023}
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