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Simplifying 44x2 + -4x + 5 = 4x + 6 Reorder the terms: 5 + -4x + 44x2 = 4x + 6 Reorder the terms: 5 + -4x + 44x2 = 6 + 4x Solving 5 + -4x + 44x2 = 6 + 4x Solving for variable 'x'. Reorder the terms: 5 + -6 + -4x + -4x + 44x2 = 6 + 4x + -6 + -4x Combine like terms: 5 + -6 = -1 -1 + -4x + -4x + 44x2 = 6 + 4x + -6 + -4x Combine like terms: -4x + -4x = -8x -1 + -8x + 44x2 = 6 + 4x + -6 + -4x Reorder the terms: -1 + -8x + 44x2 = 6 + -6 + 4x + -4x Combine like terms: 6 + -6 = 0 -1 + -8x + 44x2 = 0 + 4x + -4x -1 + -8x + 44x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -1 + -8x + 44x2 = 0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.02272727273 + -0.1818181818x + x2 = 0 Move the constant term to the right: Add '0.02272727273' to each side of the equation. -0.02272727273 + -0.1818181818x + 0.02272727273 + x2 = 0 + 0.02272727273 Reorder the terms: -0.02272727273 + 0.02272727273 + -0.1818181818x + x2 = 0 + 0.02272727273 Combine like terms: -0.02272727273 + 0.02272727273 = 0.00000000000 0.00000000000 + -0.1818181818x + x2 = 0 + 0.02272727273 -0.1818181818x + x2 = 0 + 0.02272727273 Combine like terms: 0 + 0.02272727273 = 0.02272727273 -0.1818181818x + x2 = 0.02272727273 The x term is -0.1818181818x. Take half its coefficient (-0.0909090909). Square it (0.008264462808) and add it to both sides. Add '0.008264462808' to each side of the equation. -0.1818181818x + 0.008264462808 + x2 = 0.02272727273 + 0.008264462808 Reorder the terms: 0.008264462808 + -0.1818181818x + x2 = 0.02272727273 + 0.008264462808 Combine like terms: 0.02272727273 + 0.008264462808 = 0.030991735538 0.008264462808 + -0.1818181818x + x2 = 0.030991735538 Factor a perfect square on the left side: (x + -0.0909090909)(x + -0.0909090909) = 0.030991735538 Calculate the square root of the right side: 0.176044698 Break this problem into two subproblems by setting (x + -0.0909090909) equal to 0.176044698 and -0.176044698.Subproblem 1
x + -0.0909090909 = 0.176044698 Simplifying x + -0.0909090909 = 0.176044698 Reorder the terms: -0.0909090909 + x = 0.176044698 Solving -0.0909090909 + x = 0.176044698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = 0.176044698 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = 0.176044698 + 0.0909090909 x = 0.176044698 + 0.0909090909 Combine like terms: 0.176044698 + 0.0909090909 = 0.2669537889 x = 0.2669537889 Simplifying x = 0.2669537889Subproblem 2
x + -0.0909090909 = -0.176044698 Simplifying x + -0.0909090909 = -0.176044698 Reorder the terms: -0.0909090909 + x = -0.176044698 Solving -0.0909090909 + x = -0.176044698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0909090909' to each side of the equation. -0.0909090909 + 0.0909090909 + x = -0.176044698 + 0.0909090909 Combine like terms: -0.0909090909 + 0.0909090909 = 0.0000000000 0.0000000000 + x = -0.176044698 + 0.0909090909 x = -0.176044698 + 0.0909090909 Combine like terms: -0.176044698 + 0.0909090909 = -0.0851356071 x = -0.0851356071 Simplifying x = -0.0851356071Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2669537889, -0.0851356071}
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