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Simplifying 0 = x2 + 16x + -235 Reorder the terms: 0 = -235 + 16x + x2 Solving 0 = -235 + 16x + x2 Solving for variable 'x'. Combine like terms: 0 + 235 = 235 235 + -16x + -1x2 = -235 + 16x + x2 + 235 + -16x + -1x2 Reorder the terms: 235 + -16x + -1x2 = -235 + 235 + 16x + -16x + x2 + -1x2 Combine like terms: -235 + 235 = 0 235 + -16x + -1x2 = 0 + 16x + -16x + x2 + -1x2 235 + -16x + -1x2 = 16x + -16x + x2 + -1x2 Combine like terms: 16x + -16x = 0 235 + -16x + -1x2 = 0 + x2 + -1x2 235 + -16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 235 + -16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -235 + 16x + x2 = 0 Move the constant term to the right: Add '235' to each side of the equation. -235 + 16x + 235 + x2 = 0 + 235 Reorder the terms: -235 + 235 + 16x + x2 = 0 + 235 Combine like terms: -235 + 235 = 0 0 + 16x + x2 = 0 + 235 16x + x2 = 0 + 235 Combine like terms: 0 + 235 = 235 16x + x2 = 235 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 = 235 + 64 Reorder the terms: 64 + 16x + x2 = 235 + 64 Combine like terms: 235 + 64 = 299 64 + 16x + x2 = 299 Factor a perfect square on the left side: (x + 8)(x + 8) = 299 Calculate the square root of the right side: 17.291616466 Break this problem into two subproblems by setting (x + 8) equal to 17.291616466 and -17.291616466.Subproblem 1
x + 8 = 17.291616466 Simplifying x + 8 = 17.291616466 Reorder the terms: 8 + x = 17.291616466 Solving 8 + x = 17.291616466 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 = 17.291616466 + -8 Combine like terms: 8 + -8 = 0 0 + x = 17.291616466 + -8 x = 17.291616466 + -8 Combine like terms: 17.291616466 + -8 = 9.291616466 x = 9.291616466 Simplifying x = 9.291616466Subproblem 2
x + 8 = -17.291616466 Simplifying x + 8 = -17.291616466 Reorder the terms: 8 + x = -17.291616466 Solving 8 + x = -17.291616466 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 = -17.291616466 + -8 Combine like terms: 8 + -8 = 0 0 + x = -17.291616466 + -8 x = -17.291616466 + -8 Combine like terms: -17.291616466 + -8 = -25.291616466 x = -25.291616466 Simplifying x = -25.291616466Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.291616466, -25.291616466}
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