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Simplifying 44x2 + 55x + 6 = 0 Reorder the terms: 6 + 55x + 44x2 = 0 Solving 6 + 55x + 44x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. 0.1363636364 + 1.25x + x2 = 0 Move the constant term to the right: Add '-0.1363636364' to each side of the equation. 0.1363636364 + 1.25x + -0.1363636364 + x2 = 0 + -0.1363636364 Reorder the terms: 0.1363636364 + -0.1363636364 + 1.25x + x2 = 0 + -0.1363636364 Combine like terms: 0.1363636364 + -0.1363636364 = 0.0000000000 0.0000000000 + 1.25x + x2 = 0 + -0.1363636364 1.25x + x2 = 0 + -0.1363636364 Combine like terms: 0 + -0.1363636364 = -0.1363636364 1.25x + x2 = -0.1363636364 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = -0.1363636364 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = -0.1363636364 + 0.390625 Combine like terms: -0.1363636364 + 0.390625 = 0.2542613636 0.390625 + 1.25x + x2 = 0.2542613636 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 0.2542613636 Calculate the square root of the right side: 0.504243358 Break this problem into two subproblems by setting (x + 0.625) equal to 0.504243358 and -0.504243358.Subproblem 1
x + 0.625 = 0.504243358 Simplifying x + 0.625 = 0.504243358 Reorder the terms: 0.625 + x = 0.504243358 Solving 0.625 + x = 0.504243358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.504243358 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.504243358 + -0.625 x = 0.504243358 + -0.625 Combine like terms: 0.504243358 + -0.625 = -0.120756642 x = -0.120756642 Simplifying x = -0.120756642Subproblem 2
x + 0.625 = -0.504243358 Simplifying x + 0.625 = -0.504243358 Reorder the terms: 0.625 + x = -0.504243358 Solving 0.625 + x = -0.504243358 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.504243358 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.504243358 + -0.625 x = -0.504243358 + -0.625 Combine like terms: -0.504243358 + -0.625 = -1.129243358 x = -1.129243358 Simplifying x = -1.129243358Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.120756642, -1.129243358}
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