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Simplifying 15(x + 8) + 15 = 2x(x + 8) Reorder the terms: 15(8 + x) + 15 = 2x(x + 8) (8 * 15 + x * 15) + 15 = 2x(x + 8) (120 + 15x) + 15 = 2x(x + 8) Reorder the terms: 120 + 15 + 15x = 2x(x + 8) Combine like terms: 120 + 15 = 135 135 + 15x = 2x(x + 8) Reorder the terms: 135 + 15x = 2x(8 + x) 135 + 15x = (8 * 2x + x * 2x) 135 + 15x = (16x + 2x2) Solving 135 + 15x = 16x + 2x2 Solving for variable 'x'. Combine like terms: 15x + -16x = -1x 135 + -1x + -2x2 = 16x + 2x2 + -16x + -2x2 Reorder the terms: 135 + -1x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 135 + -1x + -2x2 = 0 + 2x2 + -2x2 135 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 135 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -67.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '67.5' to each side of the equation. -67.5 + 0.5x + 67.5 + x2 = 0 + 67.5 Reorder the terms: -67.5 + 67.5 + 0.5x + x2 = 0 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + 0.5x + x2 = 0 + 67.5 0.5x + x2 = 0 + 67.5 Combine like terms: 0 + 67.5 = 67.5 0.5x + x2 = 67.5 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 67.5 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 67.5 + 0.0625 Combine like terms: 67.5 + 0.0625 = 67.5625 0.0625 + 0.5x + x2 = 67.5625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 67.5625 Calculate the square root of the right side: 8.219641111 Break this problem into two subproblems by setting (x + 0.25) equal to 8.219641111 and -8.219641111.Subproblem 1
x + 0.25 = 8.219641111 Simplifying x + 0.25 = 8.219641111 Reorder the terms: 0.25 + x = 8.219641111 Solving 0.25 + x = 8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 8.219641111 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 8.219641111 + -0.25 x = 8.219641111 + -0.25 Combine like terms: 8.219641111 + -0.25 = 7.969641111 x = 7.969641111 Simplifying x = 7.969641111Subproblem 2
x + 0.25 = -8.219641111 Simplifying x + 0.25 = -8.219641111 Reorder the terms: 0.25 + x = -8.219641111 Solving 0.25 + x = -8.219641111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -8.219641111 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -8.219641111 + -0.25 x = -8.219641111 + -0.25 Combine like terms: -8.219641111 + -0.25 = -8.469641111 x = -8.469641111 Simplifying x = -8.469641111Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.969641111, -8.469641111}
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