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Simplifying 2x2 + 5x + 7 = 3 + -6x Reorder the terms: 7 + 5x + 2x2 = 3 + -6x Solving 7 + 5x + 2x2 = 3 + -6x Solving for variable 'x'. Reorder the terms: 7 + -3 + 5x + 6x + 2x2 = 3 + -6x + -3 + 6x Combine like terms: 7 + -3 = 4 4 + 5x + 6x + 2x2 = 3 + -6x + -3 + 6x Combine like terms: 5x + 6x = 11x 4 + 11x + 2x2 = 3 + -6x + -3 + 6x Reorder the terms: 4 + 11x + 2x2 = 3 + -3 + -6x + 6x Combine like terms: 3 + -3 = 0 4 + 11x + 2x2 = 0 + -6x + 6x 4 + 11x + 2x2 = -6x + 6x Combine like terms: -6x + 6x = 0 4 + 11x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2 + 5.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 5.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 5.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5.5x + x2 = 0 + -2 5.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 5.5x + x2 = -2 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = -2 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -2 + 7.5625 Combine like terms: -2 + 7.5625 = 5.5625 7.5625 + 5.5x + x2 = 5.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (x + 2.75) equal to 2.358495283 and -2.358495283.Subproblem 1
x + 2.75 = 2.358495283 Simplifying x + 2.75 = 2.358495283 Reorder the terms: 2.75 + x = 2.358495283 Solving 2.75 + x = 2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 2.358495283 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 2.358495283 + -2.75 x = 2.358495283 + -2.75 Combine like terms: 2.358495283 + -2.75 = -0.391504717 x = -0.391504717 Simplifying x = -0.391504717Subproblem 2
x + 2.75 = -2.358495283 Simplifying x + 2.75 = -2.358495283 Reorder the terms: 2.75 + x = -2.358495283 Solving 2.75 + x = -2.358495283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -2.358495283 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -2.358495283 + -2.75 x = -2.358495283 + -2.75 Combine like terms: -2.358495283 + -2.75 = -5.108495283 x = -5.108495283 Simplifying x = -5.108495283Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.391504717, -5.108495283}
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