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Simplifying (6x2 + 9x + -2) + (8x2 + 4x + -6) = 0 Reorder the terms: (-2 + 9x + 6x2) + (8x2 + 4x + -6) = 0 Remove parenthesis around (-2 + 9x + 6x2) -2 + 9x + 6x2 + (8x2 + 4x + -6) = 0 Reorder the terms: -2 + 9x + 6x2 + (-6 + 4x + 8x2) = 0 Remove parenthesis around (-6 + 4x + 8x2) -2 + 9x + 6x2 + -6 + 4x + 8x2 = 0 Reorder the terms: -2 + -6 + 9x + 4x + 6x2 + 8x2 = 0 Combine like terms: -2 + -6 = -8 -8 + 9x + 4x + 6x2 + 8x2 = 0 Combine like terms: 9x + 4x = 13x -8 + 13x + 6x2 + 8x2 = 0 Combine like terms: 6x2 + 8x2 = 14x2 -8 + 13x + 14x2 = 0 Solving -8 + 13x + 14x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. -0.5714285714 + 0.9285714286x + x2 = 0 Move the constant term to the right: Add '0.5714285714' to each side of the equation. -0.5714285714 + 0.9285714286x + 0.5714285714 + x2 = 0 + 0.5714285714 Reorder the terms: -0.5714285714 + 0.5714285714 + 0.9285714286x + x2 = 0 + 0.5714285714 Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000 0.0000000000 + 0.9285714286x + x2 = 0 + 0.5714285714 0.9285714286x + x2 = 0 + 0.5714285714 Combine like terms: 0 + 0.5714285714 = 0.5714285714 0.9285714286x + x2 = 0.5714285714 The x term is 0.9285714286x. Take half its coefficient (0.4642857143). Square it (0.2155612245) and add it to both sides. Add '0.2155612245' to each side of the equation. 0.9285714286x + 0.2155612245 + x2 = 0.5714285714 + 0.2155612245 Reorder the terms: 0.2155612245 + 0.9285714286x + x2 = 0.5714285714 + 0.2155612245 Combine like terms: 0.5714285714 + 0.2155612245 = 0.7869897959 0.2155612245 + 0.9285714286x + x2 = 0.7869897959 Factor a perfect square on the left side: (x + 0.4642857143)(x + 0.4642857143) = 0.7869897959 Calculate the square root of the right side: 0.887124453 Break this problem into two subproblems by setting (x + 0.4642857143) equal to 0.887124453 and -0.887124453.Subproblem 1
x + 0.4642857143 = 0.887124453 Simplifying x + 0.4642857143 = 0.887124453 Reorder the terms: 0.4642857143 + x = 0.887124453 Solving 0.4642857143 + x = 0.887124453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = 0.887124453 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = 0.887124453 + -0.4642857143 x = 0.887124453 + -0.4642857143 Combine like terms: 0.887124453 + -0.4642857143 = 0.4228387387 x = 0.4228387387 Simplifying x = 0.4228387387Subproblem 2
x + 0.4642857143 = -0.887124453 Simplifying x + 0.4642857143 = -0.887124453 Reorder the terms: 0.4642857143 + x = -0.887124453 Solving 0.4642857143 + x = -0.887124453 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4642857143' to each side of the equation. 0.4642857143 + -0.4642857143 + x = -0.887124453 + -0.4642857143 Combine like terms: 0.4642857143 + -0.4642857143 = 0.0000000000 0.0000000000 + x = -0.887124453 + -0.4642857143 x = -0.887124453 + -0.4642857143 Combine like terms: -0.887124453 + -0.4642857143 = -1.3514101673 x = -1.3514101673 Simplifying x = -1.3514101673Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4228387387, -1.3514101673}
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