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Simplifying 6x2 + 3x + -26 = 0 Reorder the terms: -26 + 3x + 6x2 = 0 Solving -26 + 3x + 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'. -4.333333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '4.333333333' to each side of the equation. -4.333333333 + 0.5x + 4.333333333 + x2 = 0 + 4.333333333 Reorder the terms: -4.333333333 + 4.333333333 + 0.5x + x2 = 0 + 4.333333333 Combine like terms: -4.333333333 + 4.333333333 = 0.000000000 0.000000000 + 0.5x + x2 = 0 + 4.333333333 0.5x + x2 = 0 + 4.333333333 Combine like terms: 0 + 4.333333333 = 4.333333333 0.5x + x2 = 4.333333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 4.333333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 4.333333333 + 0.0625 Combine like terms: 4.333333333 + 0.0625 = 4.395833333 0.0625 + 0.5x + x2 = 4.395833333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 4.395833333 Calculate the square root of the right side: 2.096624271 Break this problem into two subproblems by setting (x + 0.25) equal to 2.096624271 and -2.096624271.Subproblem 1
x + 0.25 = 2.096624271 Simplifying x + 0.25 = 2.096624271 Reorder the terms: 0.25 + x = 2.096624271 Solving 0.25 + x = 2.096624271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 2.096624271 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.096624271 + -0.25 x = 2.096624271 + -0.25 Combine like terms: 2.096624271 + -0.25 = 1.846624271 x = 1.846624271 Simplifying x = 1.846624271Subproblem 2
x + 0.25 = -2.096624271 Simplifying x + 0.25 = -2.096624271 Reorder the terms: 0.25 + x = -2.096624271 Solving 0.25 + x = -2.096624271 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -2.096624271 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.096624271 + -0.25 x = -2.096624271 + -0.25 Combine like terms: -2.096624271 + -0.25 = -2.346624271 x = -2.346624271 Simplifying x = -2.346624271Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.846624271, -2.346624271}
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