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Simplifying 90 = (x + -10) * x Reorder the terms: 90 = (-10 + x) * x Reorder the terms for easier multiplication: 90 = x(-10 + x) 90 = (-10 * x + x * x) 90 = (-10x + x2) Solving 90 = -10x + x2 Solving for variable 'x'. Reorder the terms: 90 + 10x + -1x2 = -10x + 10x + x2 + -1x2 Combine like terms: -10x + 10x = 0 90 + 10x + -1x2 = 0 + x2 + -1x2 90 + 10x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 90 + 10x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -90 + -10x + x2 = 0 Move the constant term to the right: Add '90' to each side of the equation. -90 + -10x + 90 + x2 = 0 + 90 Reorder the terms: -90 + 90 + -10x + x2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + -10x + x2 = 0 + 90 -10x + x2 = 0 + 90 Combine like terms: 0 + 90 = 90 -10x + x2 = 90 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 90 + 25 Reorder the terms: 25 + -10x + x2 = 90 + 25 Combine like terms: 90 + 25 = 115 25 + -10x + x2 = 115 Factor a perfect square on the left side: (x + -5)(x + -5) = 115 Calculate the square root of the right side: 10.723805295 Break this problem into two subproblems by setting (x + -5) equal to 10.723805295 and -10.723805295.Subproblem 1
x + -5 = 10.723805295 Simplifying x + -5 = 10.723805295 Reorder the terms: -5 + x = 10.723805295 Solving -5 + x = 10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.723805295 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.723805295 + 5 x = 10.723805295 + 5 Combine like terms: 10.723805295 + 5 = 15.723805295 x = 15.723805295 Simplifying x = 15.723805295Subproblem 2
x + -5 = -10.723805295 Simplifying x + -5 = -10.723805295 Reorder the terms: -5 + x = -10.723805295 Solving -5 + x = -10.723805295 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.723805295 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.723805295 + 5 x = -10.723805295 + 5 Combine like terms: -10.723805295 + 5 = -5.723805295 x = -5.723805295 Simplifying x = -5.723805295Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.723805295, -5.723805295}
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