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Simplifying x2 + 17x + 74 = 10 Reorder the terms: 74 + 17x + x2 = 10 Solving 74 + 17x + x2 = 10 Solving for variable 'x'. Reorder the terms: 74 + -10 + 17x + x2 = 10 + -10 Combine like terms: 74 + -10 = 64 64 + 17x + x2 = 10 + -10 Combine like terms: 10 + -10 = 0 64 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + 17x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + 17x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + 17x + x2 = 0 + -64 17x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 17x + x2 = -64 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 = -64 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -64 + 72.25 Combine like terms: -64 + 72.25 = 8.25 72.25 + 17x + x2 = 8.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (x + 8.5) equal to 2.872281323 and -2.872281323.Subproblem 1
x + 8.5 = 2.872281323 Simplifying x + 8.5 = 2.872281323 Reorder the terms: 8.5 + x = 2.872281323 Solving 8.5 + x = 2.872281323 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 = 2.872281323 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 2.872281323 + -8.5 x = 2.872281323 + -8.5 Combine like terms: 2.872281323 + -8.5 = -5.627718677 x = -5.627718677 Simplifying x = -5.627718677Subproblem 2
x + 8.5 = -2.872281323 Simplifying x + 8.5 = -2.872281323 Reorder the terms: 8.5 + x = -2.872281323 Solving 8.5 + x = -2.872281323 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 = -2.872281323 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -2.872281323 + -8.5 x = -2.872281323 + -8.5 Combine like terms: -2.872281323 + -8.5 = -11.372281323 x = -11.372281323 Simplifying x = -11.372281323Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.627718677, -11.372281323}
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