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Simplifying 36 = x(15 + x) 36 = (15 * x + x * x) 36 = (15x + x2) Solving 36 = 15x + x2 Solving for variable 'x'. Reorder the terms: 36 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 36 + -15x + -1x2 = 0 + x2 + -1x2 36 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 36 + -15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -36 + 15x + x2 = 0 Move the constant term to the right: Add '36' to each side of the equation. -36 + 15x + 36 + x2 = 0 + 36 Reorder the terms: -36 + 36 + 15x + x2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 15x + x2 = 0 + 36 15x + x2 = 0 + 36 Combine like terms: 0 + 36 = 36 15x + x2 = 36 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 = 36 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 36 + 56.25 Combine like terms: 36 + 56.25 = 92.25 56.25 + 15x + x2 = 92.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + 7.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + 7.5 = 9.604686356 Simplifying x + 7.5 = 9.604686356 Reorder the terms: 7.5 + x = 9.604686356 Solving 7.5 + x = 9.604686356 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 = 9.604686356 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 9.604686356 + -7.5 x = 9.604686356 + -7.5 Combine like terms: 9.604686356 + -7.5 = 2.104686356 x = 2.104686356 Simplifying x = 2.104686356Subproblem 2
x + 7.5 = -9.604686356 Simplifying x + 7.5 = -9.604686356 Reorder the terms: 7.5 + x = -9.604686356 Solving 7.5 + x = -9.604686356 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 = -9.604686356 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -9.604686356 + -7.5 x = -9.604686356 + -7.5 Combine like terms: -9.604686356 + -7.5 = -17.104686356 x = -17.104686356 Simplifying x = -17.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.104686356, -17.104686356}
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