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Simplifying (15 + x) * x = 64 Reorder the terms for easier multiplication: x(15 + x) = 64 (15 * x + x * x) = 64 (15x + x2) = 64 Solving 15x + x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + 15x + x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 15x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 15x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 15x + x2 = 0 + 64 15x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 15x + x2 = 64 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 = 64 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 64 + 56.25 Combine like terms: 64 + 56.25 = 120.25 56.25 + 15x + x2 = 120.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (x + 7.5) equal to 10.9658561 and -10.9658561.Subproblem 1
x + 7.5 = 10.9658561 Simplifying x + 7.5 = 10.9658561 Reorder the terms: 7.5 + x = 10.9658561 Solving 7.5 + x = 10.9658561 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 = 10.9658561 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 10.9658561 + -7.5 x = 10.9658561 + -7.5 Combine like terms: 10.9658561 + -7.5 = 3.4658561 x = 3.4658561 Simplifying x = 3.4658561Subproblem 2
x + 7.5 = -10.9658561 Simplifying x + 7.5 = -10.9658561 Reorder the terms: 7.5 + x = -10.9658561 Solving 7.5 + x = -10.9658561 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 = -10.9658561 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -10.9658561 + -7.5 x = -10.9658561 + -7.5 Combine like terms: -10.9658561 + -7.5 = -18.4658561 x = -18.4658561 Simplifying x = -18.4658561Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4658561, -18.4658561}
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