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Simplifying 0 = x2 + 31x + -94 Reorder the terms: 0 = -94 + 31x + x2 Solving 0 = -94 + 31x + x2 Solving for variable 'x'. Combine like terms: 0 + 94 = 94 94 + -31x + -1x2 = -94 + 31x + x2 + 94 + -31x + -1x2 Reorder the terms: 94 + -31x + -1x2 = -94 + 94 + 31x + -31x + x2 + -1x2 Combine like terms: -94 + 94 = 0 94 + -31x + -1x2 = 0 + 31x + -31x + x2 + -1x2 94 + -31x + -1x2 = 31x + -31x + x2 + -1x2 Combine like terms: 31x + -31x = 0 94 + -31x + -1x2 = 0 + x2 + -1x2 94 + -31x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 94 + -31x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -94 + 31x + x2 = 0 Move the constant term to the right: Add '94' to each side of the equation. -94 + 31x + 94 + x2 = 0 + 94 Reorder the terms: -94 + 94 + 31x + x2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 31x + x2 = 0 + 94 31x + x2 = 0 + 94 Combine like terms: 0 + 94 = 94 31x + x2 = 94 The x term is 31x. Take half its coefficient (15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. 31x + 240.25 + x2 = 94 + 240.25 Reorder the terms: 240.25 + 31x + x2 = 94 + 240.25 Combine like terms: 94 + 240.25 = 334.25 240.25 + 31x + x2 = 334.25 Factor a perfect square on the left side: (x + 15.5)(x + 15.5) = 334.25 Calculate the square root of the right side: 18.282505299 Break this problem into two subproblems by setting (x + 15.5) equal to 18.282505299 and -18.282505299.Subproblem 1
x + 15.5 = 18.282505299 Simplifying x + 15.5 = 18.282505299 Reorder the terms: 15.5 + x = 18.282505299 Solving 15.5 + x = 18.282505299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = 18.282505299 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = 18.282505299 + -15.5 x = 18.282505299 + -15.5 Combine like terms: 18.282505299 + -15.5 = 2.782505299 x = 2.782505299 Simplifying x = 2.782505299Subproblem 2
x + 15.5 = -18.282505299 Simplifying x + 15.5 = -18.282505299 Reorder the terms: 15.5 + x = -18.282505299 Solving 15.5 + x = -18.282505299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + x = -18.282505299 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + x = -18.282505299 + -15.5 x = -18.282505299 + -15.5 Combine like terms: -18.282505299 + -15.5 = -33.782505299 x = -33.782505299 Simplifying x = -33.782505299Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.782505299, -33.782505299}
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