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Simplifying 4x2 + -28x + 22 = 0 Reorder the terms: 22 + -28x + 4x2 = 0 Solving 22 + -28x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + -14x + 2x2 = 0 Solving 11 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -7x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -7x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -7x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -7x + x2 = 0 + -5.5 -7x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -7x + x2 = -5.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -5.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -5.5 + 12.25 Combine like terms: -5.5 + 12.25 = 6.75 12.25 + -7x + x2 = 6.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -3.5) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -3.5 = 2.598076211 Simplifying x + -3.5 = 2.598076211 Reorder the terms: -3.5 + x = 2.598076211 Solving -3.5 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 2.598076211 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 2.598076211 + 3.5 x = 2.598076211 + 3.5 Combine like terms: 2.598076211 + 3.5 = 6.098076211 x = 6.098076211 Simplifying x = 6.098076211Subproblem 2
x + -3.5 = -2.598076211 Simplifying x + -3.5 = -2.598076211 Reorder the terms: -3.5 + x = -2.598076211 Solving -3.5 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -2.598076211 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -2.598076211 + 3.5 x = -2.598076211 + 3.5 Combine like terms: -2.598076211 + 3.5 = 0.901923789 x = 0.901923789 Simplifying x = 0.901923789Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.098076211, 0.901923789}Solution
x = {6.098076211, 0.901923789}
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