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Simplifying 6x2 + 9x + -35 = 0 Reorder the terms: -35 + 9x + 6x2 = 0 Solving -35 + 9x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.833333333 + 1.5x + x2 = 0 Move the constant term to the right: Add '5.833333333' to each side of the equation. -5.833333333 + 1.5x + 5.833333333 + x2 = 0 + 5.833333333 Reorder the terms: -5.833333333 + 5.833333333 + 1.5x + x2 = 0 + 5.833333333 Combine like terms: -5.833333333 + 5.833333333 = 0.000000000 0.000000000 + 1.5x + x2 = 0 + 5.833333333 1.5x + x2 = 0 + 5.833333333 Combine like terms: 0 + 5.833333333 = 5.833333333 1.5x + x2 = 5.833333333 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = 5.833333333 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = 5.833333333 + 0.5625 Combine like terms: 5.833333333 + 0.5625 = 6.395833333 0.5625 + 1.5x + x2 = 6.395833333 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = 6.395833333 Calculate the square root of the right side: 2.528998484 Break this problem into two subproblems by setting (x + 0.75) equal to 2.528998484 and -2.528998484.Subproblem 1
x + 0.75 = 2.528998484 Simplifying x + 0.75 = 2.528998484 Reorder the terms: 0.75 + x = 2.528998484 Solving 0.75 + x = 2.528998484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = 2.528998484 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = 2.528998484 + -0.75 x = 2.528998484 + -0.75 Combine like terms: 2.528998484 + -0.75 = 1.778998484 x = 1.778998484 Simplifying x = 1.778998484Subproblem 2
x + 0.75 = -2.528998484 Simplifying x + 0.75 = -2.528998484 Reorder the terms: 0.75 + x = -2.528998484 Solving 0.75 + x = -2.528998484 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + x = -2.528998484 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + x = -2.528998484 + -0.75 x = -2.528998484 + -0.75 Combine like terms: -2.528998484 + -0.75 = -3.278998484 x = -3.278998484 Simplifying x = -3.278998484Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.778998484, -3.278998484}
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