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Simplifying 4x2 + 9x + -6 = 8 Reorder the terms: -6 + 9x + 4x2 = 8 Solving -6 + 9x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -6 + -8 + 9x + 4x2 = 8 + -8 Combine like terms: -6 + -8 = -14 -14 + 9x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -14 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.5 + 2.25x + x2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 2.25x + 3.5 + x2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 2.25x + x2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 2.25x + x2 = 0 + 3.5 2.25x + x2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 2.25x + x2 = 3.5 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = 3.5 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 3.5 + 1.265625 Combine like terms: 3.5 + 1.265625 = 4.765625 1.265625 + 2.25x + x2 = 4.765625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 4.765625 Calculate the square root of the right side: 2.18303115 Break this problem into two subproblems by setting (x + 1.125) equal to 2.18303115 and -2.18303115.Subproblem 1
x + 1.125 = 2.18303115 Simplifying x + 1.125 = 2.18303115 Reorder the terms: 1.125 + x = 2.18303115 Solving 1.125 + x = 2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 2.18303115 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 2.18303115 + -1.125 x = 2.18303115 + -1.125 Combine like terms: 2.18303115 + -1.125 = 1.05803115 x = 1.05803115 Simplifying x = 1.05803115Subproblem 2
x + 1.125 = -2.18303115 Simplifying x + 1.125 = -2.18303115 Reorder the terms: 1.125 + x = -2.18303115 Solving 1.125 + x = -2.18303115 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -2.18303115 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -2.18303115 + -1.125 x = -2.18303115 + -1.125 Combine like terms: -2.18303115 + -1.125 = -3.30803115 x = -3.30803115 Simplifying x = -3.30803115Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.05803115, -3.30803115}
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