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Simplifying x2 + 16x + -89 = 10 Reorder the terms: -89 + 16x + x2 = 10 Solving -89 + 16x + x2 = 10 Solving for variable 'x'. Reorder the terms: -89 + -10 + 16x + x2 = 10 + -10 Combine like terms: -89 + -10 = -99 -99 + 16x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -99 + 16x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '99' to each side of the equation. -99 + 16x + 99 + x2 = 0 + 99 Reorder the terms: -99 + 99 + 16x + x2 = 0 + 99 Combine like terms: -99 + 99 = 0 0 + 16x + x2 = 0 + 99 16x + x2 = 0 + 99 Combine like terms: 0 + 99 = 99 16x + x2 = 99 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 = 99 + 64 Reorder the terms: 64 + 16x + x2 = 99 + 64 Combine like terms: 99 + 64 = 163 64 + 16x + x2 = 163 Factor a perfect square on the left side: (x + 8)(x + 8) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + 8) equal to 12.767145335 and -12.767145335.Subproblem 1
x + 8 = 12.767145335 Simplifying x + 8 = 12.767145335 Reorder the terms: 8 + x = 12.767145335 Solving 8 + x = 12.767145335 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 = 12.767145335 + -8 Combine like terms: 8 + -8 = 0 0 + x = 12.767145335 + -8 x = 12.767145335 + -8 Combine like terms: 12.767145335 + -8 = 4.767145335 x = 4.767145335 Simplifying x = 4.767145335Subproblem 2
x + 8 = -12.767145335 Simplifying x + 8 = -12.767145335 Reorder the terms: 8 + x = -12.767145335 Solving 8 + x = -12.767145335 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 = -12.767145335 + -8 Combine like terms: 8 + -8 = 0 0 + x = -12.767145335 + -8 x = -12.767145335 + -8 Combine like terms: -12.767145335 + -8 = -20.767145335 x = -20.767145335 Simplifying x = -20.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.767145335, -20.767145335}
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