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Simplifying 0 = x2 + 17x + -70 Reorder the terms: 0 = -70 + 17x + x2 Solving 0 = -70 + 17x + x2 Solving for variable 'x'. Combine like terms: 0 + 70 = 70 70 + -17x + -1x2 = -70 + 17x + x2 + 70 + -17x + -1x2 Reorder the terms: 70 + -17x + -1x2 = -70 + 70 + 17x + -17x + x2 + -1x2 Combine like terms: -70 + 70 = 0 70 + -17x + -1x2 = 0 + 17x + -17x + x2 + -1x2 70 + -17x + -1x2 = 17x + -17x + x2 + -1x2 Combine like terms: 17x + -17x = 0 70 + -17x + -1x2 = 0 + x2 + -1x2 70 + -17x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 70 + -17x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -70 + 17x + x2 = 0 Move the constant term to the right: Add '70' to each side of the equation. -70 + 17x + 70 + x2 = 0 + 70 Reorder the terms: -70 + 70 + 17x + x2 = 0 + 70 Combine like terms: -70 + 70 = 0 0 + 17x + x2 = 0 + 70 17x + x2 = 0 + 70 Combine like terms: 0 + 70 = 70 17x + x2 = 70 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 70 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 70 + 72.25 Combine like terms: 70 + 72.25 = 142.25 72.25 + 17x + x2 = 142.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 142.25 Calculate the square root of the right side: 11.926860442 Break this problem into two subproblems by setting (x + 8.5) equal to 11.926860442 and -11.926860442.Subproblem 1
x + 8.5 = 11.926860442 Simplifying x + 8.5 = 11.926860442 Reorder the terms: 8.5 + x = 11.926860442 Solving 8.5 + x = 11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 11.926860442 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 11.926860442 + -8.5 x = 11.926860442 + -8.5 Combine like terms: 11.926860442 + -8.5 = 3.426860442 x = 3.426860442 Simplifying x = 3.426860442Subproblem 2
x + 8.5 = -11.926860442 Simplifying x + 8.5 = -11.926860442 Reorder the terms: 8.5 + x = -11.926860442 Solving 8.5 + x = -11.926860442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -11.926860442 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -11.926860442 + -8.5 x = -11.926860442 + -8.5 Combine like terms: -11.926860442 + -8.5 = -20.426860442 x = -20.426860442 Simplifying x = -20.426860442Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.426860442, -20.426860442}
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