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Simplifying 4x2 + -27x + 22 = 0 Reorder the terms: 22 + -27x + 4x2 = 0 Solving 22 + -27x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.5 + -6.75x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -6.75x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -6.75x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -6.75x + x2 = 0 + -5.5 -6.75x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -6.75x + x2 = -5.5 The x term is -6.75x. Take half its coefficient (-3.375). Square it (11.390625) and add it to both sides. Add '11.390625' to each side of the equation. -6.75x + 11.390625 + x2 = -5.5 + 11.390625 Reorder the terms: 11.390625 + -6.75x + x2 = -5.5 + 11.390625 Combine like terms: -5.5 + 11.390625 = 5.890625 11.390625 + -6.75x + x2 = 5.890625 Factor a perfect square on the left side: (x + -3.375)(x + -3.375) = 5.890625 Calculate the square root of the right side: 2.42706098 Break this problem into two subproblems by setting (x + -3.375) equal to 2.42706098 and -2.42706098.Subproblem 1
x + -3.375 = 2.42706098 Simplifying x + -3.375 = 2.42706098 Reorder the terms: -3.375 + x = 2.42706098 Solving -3.375 + x = 2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = 2.42706098 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = 2.42706098 + 3.375 x = 2.42706098 + 3.375 Combine like terms: 2.42706098 + 3.375 = 5.80206098 x = 5.80206098 Simplifying x = 5.80206098Subproblem 2
x + -3.375 = -2.42706098 Simplifying x + -3.375 = -2.42706098 Reorder the terms: -3.375 + x = -2.42706098 Solving -3.375 + x = -2.42706098 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.375' to each side of the equation. -3.375 + 3.375 + x = -2.42706098 + 3.375 Combine like terms: -3.375 + 3.375 = 0.000 0.000 + x = -2.42706098 + 3.375 x = -2.42706098 + 3.375 Combine like terms: -2.42706098 + 3.375 = 0.94793902 x = 0.94793902 Simplifying x = 0.94793902Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.80206098, 0.94793902}
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