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Simplifying 10(10 + 8) = x(x + 9) Combine like terms: 10 + 8 = 18 10(18) = x(x + 9) Multiply 10 * 18 180 = x(x + 9) Reorder the terms: 180 = x(9 + x) 180 = (9 * x + x * x) 180 = (9x + x2) Solving 180 = 9x + x2 Solving for variable 'x'. Reorder the terms: 180 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 180 + -9x + -1x2 = 0 + x2 + -1x2 180 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 180 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -180 + 9x + x2 = 0 Move the constant term to the right: Add '180' to each side of the equation. -180 + 9x + 180 + x2 = 0 + 180 Reorder the terms: -180 + 180 + 9x + x2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 9x + x2 = 0 + 180 9x + x2 = 0 + 180 Combine like terms: 0 + 180 = 180 9x + x2 = 180 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 = 180 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 180 + 20.25 Combine like terms: 180 + 20.25 = 200.25 20.25 + 9x + x2 = 200.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 4.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 4.5 = 14.150971698 Simplifying x + 4.5 = 14.150971698 Reorder the terms: 4.5 + x = 14.150971698 Solving 4.5 + x = 14.150971698 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 = 14.150971698 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 14.150971698 + -4.5 x = 14.150971698 + -4.5 Combine like terms: 14.150971698 + -4.5 = 9.650971698 x = 9.650971698 Simplifying x = 9.650971698Subproblem 2
x + 4.5 = -14.150971698 Simplifying x + 4.5 = -14.150971698 Reorder the terms: 4.5 + x = -14.150971698 Solving 4.5 + x = -14.150971698 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 = -14.150971698 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -14.150971698 + -4.5 x = -14.150971698 + -4.5 Combine like terms: -14.150971698 + -4.5 = -18.650971698 x = -18.650971698 Simplifying x = -18.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.650971698, -18.650971698}
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