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Simplifying (6x2 + 5x + 7) + -1(2x2 + -11x + 12) = 0 Reorder the terms: (7 + 5x + 6x2) + -1(2x2 + -11x + 12) = 0 Remove parenthesis around (7 + 5x + 6x2) 7 + 5x + 6x2 + -1(2x2 + -11x + 12) = 0 Reorder the terms: 7 + 5x + 6x2 + -1(12 + -11x + 2x2) = 0 7 + 5x + 6x2 + (12 * -1 + -11x * -1 + 2x2 * -1) = 0 7 + 5x + 6x2 + (-12 + 11x + -2x2) = 0 Reorder the terms: 7 + -12 + 5x + 11x + 6x2 + -2x2 = 0 Combine like terms: 7 + -12 = -5 -5 + 5x + 11x + 6x2 + -2x2 = 0 Combine like terms: 5x + 11x = 16x -5 + 16x + 6x2 + -2x2 = 0 Combine like terms: 6x2 + -2x2 = 4x2 -5 + 16x + 4x2 = 0 Solving -5 + 16x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + 4x + x2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 4x + 1.25 + x2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 4x + x2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 4x + x2 = 0 + 1.25 4x + x2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 4x + x2 = 1.25 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 1.25 + 4 Reorder the terms: 4 + 4x + x2 = 1.25 + 4 Combine like terms: 1.25 + 4 = 5.25 4 + 4x + x2 = 5.25 Factor a perfect square on the left side: (x + 2)(x + 2) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 2) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 2 = 2.291287847 Simplifying x + 2 = 2.291287847 Reorder the terms: 2 + x = 2.291287847 Solving 2 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.291287847 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.291287847 + -2 x = 2.291287847 + -2 Combine like terms: 2.291287847 + -2 = 0.291287847 x = 0.291287847 Simplifying x = 0.291287847Subproblem 2
x + 2 = -2.291287847 Simplifying x + 2 = -2.291287847 Reorder the terms: 2 + x = -2.291287847 Solving 2 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.291287847 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.291287847 + -2 x = -2.291287847 + -2 Combine like terms: -2.291287847 + -2 = -4.291287847 x = -4.291287847 Simplifying x = -4.291287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.291287847, -4.291287847}
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