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Simplifying (2x2 + 5x + -7) + -1(-6x + 5) = 0 Reorder the terms: (-7 + 5x + 2x2) + -1(-6x + 5) = 0 Remove parenthesis around (-7 + 5x + 2x2) -7 + 5x + 2x2 + -1(-6x + 5) = 0 Reorder the terms: -7 + 5x + 2x2 + -1(5 + -6x) = 0 -7 + 5x + 2x2 + (5 * -1 + -6x * -1) = 0 -7 + 5x + 2x2 + (-5 + 6x) = 0 Reorder the terms: -7 + -5 + 5x + 6x + 2x2 = 0 Combine like terms: -7 + -5 = -12 -12 + 5x + 6x + 2x2 = 0 Combine like terms: 5x + 6x = 11x -12 + 11x + 2x2 = 0 Solving -12 + 11x + 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'. -6 + 5.5x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 5.5x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 5.5x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 5.5x + x2 = 0 + 6 5.5x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 5.5x + x2 = 6 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 = 6 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 6 + 7.5625 Combine like terms: 6 + 7.5625 = 13.5625 7.5625 + 5.5x + x2 = 13.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 13.5625 Calculate the square root of the right side: 3.682729966 Break this problem into two subproblems by setting (x + 2.75) equal to 3.682729966 and -3.682729966.Subproblem 1
x + 2.75 = 3.682729966 Simplifying x + 2.75 = 3.682729966 Reorder the terms: 2.75 + x = 3.682729966 Solving 2.75 + x = 3.682729966 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 = 3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 3.682729966 + -2.75 x = 3.682729966 + -2.75 Combine like terms: 3.682729966 + -2.75 = 0.932729966 x = 0.932729966 Simplifying x = 0.932729966Subproblem 2
x + 2.75 = -3.682729966 Simplifying x + 2.75 = -3.682729966 Reorder the terms: 2.75 + x = -3.682729966 Solving 2.75 + x = -3.682729966 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 = -3.682729966 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -3.682729966 + -2.75 x = -3.682729966 + -2.75 Combine like terms: -3.682729966 + -2.75 = -6.432729966 x = -6.432729966 Simplifying x = -6.432729966Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.932729966, -6.432729966}
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