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Simplifying x(15 + -1x) = 11 (15 * x + -1x * x) = 11 (15x + -1x2) = 11 Solving 15x + -1x2 = 11 Solving for variable 'x'. Reorder the terms: -11 + 15x + -1x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 11 + -15x + x2 = 0 Move the constant term to the right: Add '-11' to each side of the equation. 11 + -15x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -15x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -15x + x2 = 0 + -11 -15x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -15x + x2 = -11 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 = -11 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -11 + 56.25 Combine like terms: -11 + 56.25 = 45.25 56.25 + -15x + x2 = 45.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + -7.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + -7.5 = 6.726812024 Simplifying x + -7.5 = 6.726812024 Reorder the terms: -7.5 + x = 6.726812024 Solving -7.5 + x = 6.726812024 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 = 6.726812024 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 6.726812024 + 7.5 x = 6.726812024 + 7.5 Combine like terms: 6.726812024 + 7.5 = 14.226812024 x = 14.226812024 Simplifying x = 14.226812024Subproblem 2
x + -7.5 = -6.726812024 Simplifying x + -7.5 = -6.726812024 Reorder the terms: -7.5 + x = -6.726812024 Solving -7.5 + x = -6.726812024 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 = -6.726812024 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -6.726812024 + 7.5 x = -6.726812024 + 7.5 Combine like terms: -6.726812024 + 7.5 = 0.773187976 x = 0.773187976 Simplifying x = 0.773187976Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.226812024, 0.773187976}
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