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Simplifying 4x2 + -34x + 22 = 0 Reorder the terms: 22 + -34x + 4x2 = 0 Solving 22 + -34x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -17x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -17x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + -17x + 2x2 = 0 Solving 11 + -17x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + -8.5x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -8.5x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -8.5x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -8.5x + x2 = 0 + -5.5 -8.5x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -8.5x + x2 = -5.5 The x term is -8.5x. Take half its coefficient (-4.25). Square it (18.0625) and add it to both sides. Add '18.0625' to each side of the equation. -8.5x + 18.0625 + x2 = -5.5 + 18.0625 Reorder the terms: 18.0625 + -8.5x + x2 = -5.5 + 18.0625 Combine like terms: -5.5 + 18.0625 = 12.5625 18.0625 + -8.5x + x2 = 12.5625 Factor a perfect square on the left side: (x + -4.25)(x + -4.25) = 12.5625 Calculate the square root of the right side: 3.54436172 Break this problem into two subproblems by setting (x + -4.25) equal to 3.54436172 and -3.54436172.Subproblem 1
x + -4.25 = 3.54436172 Simplifying x + -4.25 = 3.54436172 Reorder the terms: -4.25 + x = 3.54436172 Solving -4.25 + x = 3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = 3.54436172 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = 3.54436172 + 4.25 x = 3.54436172 + 4.25 Combine like terms: 3.54436172 + 4.25 = 7.79436172 x = 7.79436172 Simplifying x = 7.79436172Subproblem 2
x + -4.25 = -3.54436172 Simplifying x + -4.25 = -3.54436172 Reorder the terms: -4.25 + x = -3.54436172 Solving -4.25 + x = -3.54436172 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.25' to each side of the equation. -4.25 + 4.25 + x = -3.54436172 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + x = -3.54436172 + 4.25 x = -3.54436172 + 4.25 Combine like terms: -3.54436172 + 4.25 = 0.70563828 x = 0.70563828 Simplifying x = 0.70563828Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.79436172, 0.70563828}Solution
x = {7.79436172, 0.70563828}
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