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Simplifying x2 + -16x = -11.5 Reorder the terms: -16x + x2 = -11.5 Solving -16x + x2 = -11.5 Solving for variable 'x'. Reorder the terms: 11.5 + -16x + x2 = -11.5 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 11.5 + -16x + x2 = 0.0 Begin completing the square. Move the constant term to the right: Add '-11.5' to each side of the equation. 11.5 + -16x + -11.5 + x2 = 0.0 + -11.5 Reorder the terms: 11.5 + -11.5 + -16x + x2 = 0.0 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + -16x + x2 = 0.0 + -11.5 -16x + x2 = 0.0 + -11.5 Combine like terms: 0.0 + -11.5 = -11.5 -16x + x2 = -11.5 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 = -11.5 + 64 Reorder the terms: 64 + -16x + x2 = -11.5 + 64 Combine like terms: -11.5 + 64 = 52.5 64 + -16x + x2 = 52.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (x + -8) equal to 7.245688373 and -7.245688373.Subproblem 1
x + -8 = 7.245688373 Simplifying x + -8 = 7.245688373 Reorder the terms: -8 + x = 7.245688373 Solving -8 + x = 7.245688373 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 = 7.245688373 + 8 Combine like terms: -8 + 8 = 0 0 + x = 7.245688373 + 8 x = 7.245688373 + 8 Combine like terms: 7.245688373 + 8 = 15.245688373 x = 15.245688373 Simplifying x = 15.245688373Subproblem 2
x + -8 = -7.245688373 Simplifying x + -8 = -7.245688373 Reorder the terms: -8 + x = -7.245688373 Solving -8 + x = -7.245688373 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 = -7.245688373 + 8 Combine like terms: -8 + 8 = 0 0 + x = -7.245688373 + 8 x = -7.245688373 + 8 Combine like terms: -7.245688373 + 8 = 0.754311627 x = 0.754311627 Simplifying x = 0.754311627Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.245688373, 0.754311627}
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