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Simplifying 1x(15 + -1x) = 8.25 (15 * 1x + -1x * 1x) = 8.25 (15x + -1x2) = 8.25 Solving 15x + -1x2 = 8.25 Solving for variable 'x'. Reorder the terms: -8.25 + 15x + -1x2 = 8.25 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 -8.25 + 15x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8.25 + -15x + x2 = 0.00 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -15x + -8.25 + x2 = 0.00 + -8.25 Reorder the terms: 8.25 + -8.25 + -15x + x2 = 0.00 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -15x + x2 = 0.00 + -8.25 -15x + x2 = 0.00 + -8.25 Combine like terms: 0.00 + -8.25 = -8.25 -15x + x2 = -8.25 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -8.25 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -8.25 + 56.25 Combine like terms: -8.25 + 56.25 = 48 56.25 + -15x + x2 = 48 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (x + -7.5) equal to 6.92820323 and -6.92820323.Subproblem 1
x + -7.5 = 6.92820323 Simplifying x + -7.5 = 6.92820323 Reorder the terms: -7.5 + x = 6.92820323 Solving -7.5 + x = 6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 6.92820323 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.92820323 + 7.5 x = 6.92820323 + 7.5 Combine like terms: 6.92820323 + 7.5 = 14.42820323 x = 14.42820323 Simplifying x = 14.42820323Subproblem 2
x + -7.5 = -6.92820323 Simplifying x + -7.5 = -6.92820323 Reorder the terms: -7.5 + x = -6.92820323 Solving -7.5 + x = -6.92820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -6.92820323 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.92820323 + 7.5 x = -6.92820323 + 7.5 Combine like terms: -6.92820323 + 7.5 = 0.57179677 x = 0.57179677 Simplifying x = 0.57179677Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.42820323, 0.57179677}
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