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Simplifying 2x2 + 17x + 25 = 0 Reorder the terms: 25 + 17x + 2x2 = 0 Solving 25 + 17x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + 8.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + 8.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + 8.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + 8.5x + x2 = 0 + -12.5 8.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 8.5x + x2 = -12.5 The x term is 8.5x. Take half its coefficient (4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. 8.5x + 18.0625 + x2 = -12.5 + 18.0625 Reorder the terms: 18.0625 + 8.5x + x2 = -12.5 + 18.0625 Combine like terms: -12.5 + 18.0625 = 5.5625 18.0625 + 8.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + 4.25)(x + 4.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + 4.25) equal to 2.358495283 and -2.358495283.Subproblem 1
x + 4.25 = 2.358495283 Simplifying x + 4.25 = 2.358495283 Reorder the terms: 4.25 + x = 2.358495283 Solving 4.25 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = 2.358495283 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = 2.358495283 + -4.25 x = 2.358495283 + -4.25 Combine like terms: 2.358495283 + -4.25 = -1.891504717 x = -1.891504717 Simplifying x = -1.891504717Subproblem 2
x + 4.25 = -2.358495283 Simplifying x + 4.25 = -2.358495283 Reorder the terms: 4.25 + x = -2.358495283 Solving 4.25 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + x = -2.358495283 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + x = -2.358495283 + -4.25 x = -2.358495283 + -4.25 Combine like terms: -2.358495283 + -4.25 = -6.608495283 x = -6.608495283 Simplifying x = -6.608495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.891504717, -6.608495283}
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