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Simplifying x + 15 = x2 + -15x Reorder the terms: 15 + x = x2 + -15x Reorder the terms: 15 + x = -15x + x2 Solving 15 + x = -15x + x2 Solving for variable 'x'. Combine like terms: x + 15x = 16x 15 + 16x + -1x2 = -15x + x2 + 15x + -1x2 Reorder the terms: 15 + 16x + -1x2 = -15x + 15x + x2 + -1x2 Combine like terms: -15x + 15x = 0 15 + 16x + -1x2 = 0 + x2 + -1x2 15 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 15 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -15 + -16x + x2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -16x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + -16x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -16x + x2 = 0 + 15 -16x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 -16x + x2 = 15 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 15 + 64 Reorder the terms: 64 + -16x + x2 = 15 + 64 Combine like terms: 15 + 64 = 79 64 + -16x + x2 = 79 Factor a perfect square on the left side: (x + -8)(x + -8) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (x + -8) equal to 8.888194417 and -8.888194417.Subproblem 1
x + -8 = 8.888194417 Simplifying x + -8 = 8.888194417 Reorder the terms: -8 + x = 8.888194417 Solving -8 + x = 8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 8.888194417 + 8 Combine like terms: -8 + 8 = 0 0 + x = 8.888194417 + 8 x = 8.888194417 + 8 Combine like terms: 8.888194417 + 8 = 16.888194417 x = 16.888194417 Simplifying x = 16.888194417Subproblem 2
x + -8 = -8.888194417 Simplifying x + -8 = -8.888194417 Reorder the terms: -8 + x = -8.888194417 Solving -8 + x = -8.888194417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -8.888194417 + 8 Combine like terms: -8 + 8 = 0 0 + x = -8.888194417 + 8 x = -8.888194417 + 8 Combine like terms: -8.888194417 + 8 = -0.888194417 x = -0.888194417 Simplifying x = -0.888194417Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.888194417, -0.888194417}
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