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Simplifying x2 + -15x = 108 Reorder the terms: -15x + x2 = 108 Solving -15x + x2 = 108 Solving for variable 'x'. Reorder the terms: -108 + -15x + x2 = 108 + -108 Combine like terms: 108 + -108 = 0 -108 + -15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '108' to each side of the equation. -108 + -15x + 108 + x2 = 0 + 108 Reorder the terms: -108 + 108 + -15x + x2 = 0 + 108 Combine like terms: -108 + 108 = 0 0 + -15x + x2 = 0 + 108 -15x + x2 = 0 + 108 Combine like terms: 0 + 108 = 108 -15x + x2 = 108 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 = 108 + 56.25 Reorder the terms: 56.25 + -15x + x2 = 108 + 56.25 Combine like terms: 108 + 56.25 = 164.25 56.25 + -15x + x2 = 164.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 164.25 Calculate the square root of the right side: 12.816005618 Break this problem into two subproblems by setting (x + -7.5) equal to 12.816005618 and -12.816005618.Subproblem 1
x + -7.5 = 12.816005618 Simplifying x + -7.5 = 12.816005618 Reorder the terms: -7.5 + x = 12.816005618 Solving -7.5 + x = 12.816005618 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 = 12.816005618 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 12.816005618 + 7.5 x = 12.816005618 + 7.5 Combine like terms: 12.816005618 + 7.5 = 20.316005618 x = 20.316005618 Simplifying x = 20.316005618Subproblem 2
x + -7.5 = -12.816005618 Simplifying x + -7.5 = -12.816005618 Reorder the terms: -7.5 + x = -12.816005618 Solving -7.5 + x = -12.816005618 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 = -12.816005618 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -12.816005618 + 7.5 x = -12.816005618 + 7.5 Combine like terms: -12.816005618 + 7.5 = -5.316005618 x = -5.316005618 Simplifying x = -5.316005618Solution
The solution to the problem is based on the solutions from the subproblems. x = {20.316005618, -5.316005618}
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