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Simplifying (6x2 + -4x + -5) + -1(-2x2 + -1x + 4) = 0 Reorder the terms: (-5 + -4x + 6x2) + -1(-2x2 + -1x + 4) = 0 Remove parenthesis around (-5 + -4x + 6x2) -5 + -4x + 6x2 + -1(-2x2 + -1x + 4) = 0 Reorder the terms: -5 + -4x + 6x2 + -1(4 + -1x + -2x2) = 0 -5 + -4x + 6x2 + (4 * -1 + -1x * -1 + -2x2 * -1) = 0 -5 + -4x + 6x2 + (-4 + 1x + 2x2) = 0 Reorder the terms: -5 + -4 + -4x + 1x + 6x2 + 2x2 = 0 Combine like terms: -5 + -4 = -9 -9 + -4x + 1x + 6x2 + 2x2 = 0 Combine like terms: -4x + 1x = -3x -9 + -3x + 6x2 + 2x2 = 0 Combine like terms: 6x2 + 2x2 = 8x2 -9 + -3x + 8x2 = 0 Solving -9 + -3x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + -0.375x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.375x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.375x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.375x + x2 = 0 + 1.125 -0.375x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.375x + x2 = 1.125 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 1.125 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 1.125 + 0.03515625 Combine like terms: 1.125 + 0.03515625 = 1.16015625 0.03515625 + -0.375x + x2 = 1.16015625 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 1.16015625 Calculate the square root of the right side: 1.077105496 Break this problem into two subproblems by setting (x + -0.1875) equal to 1.077105496 and -1.077105496.Subproblem 1
x + -0.1875 = 1.077105496 Simplifying x + -0.1875 = 1.077105496 Reorder the terms: -0.1875 + x = 1.077105496 Solving -0.1875 + x = 1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 1.077105496 + 0.1875 x = 1.077105496 + 0.1875 Combine like terms: 1.077105496 + 0.1875 = 1.264605496 x = 1.264605496 Simplifying x = 1.264605496Subproblem 2
x + -0.1875 = -1.077105496 Simplifying x + -0.1875 = -1.077105496 Reorder the terms: -0.1875 + x = -1.077105496 Solving -0.1875 + x = -1.077105496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -1.077105496 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -1.077105496 + 0.1875 x = -1.077105496 + 0.1875 Combine like terms: -1.077105496 + 0.1875 = -0.889605496 x = -0.889605496 Simplifying x = -0.889605496Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.264605496, -0.889605496}
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