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Simplifying 2x2 + -22x + 16 = 0 Reorder the terms: 16 + -22x + 2x2 = 0 Solving 16 + -22x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + -11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + -11x + x2)' equal to zero and attempt to solve: Simplifying 8 + -11x + x2 = 0 Solving 8 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-8' to each side of the equation. 8 + -11x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -11x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -11x + x2 = 0 + -8 -11x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -11x + x2 = -8 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -8 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -8 + 30.25 Combine like terms: -8 + 30.25 = 22.25 30.25 + -11x + x2 = 22.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (x + -5.5) equal to 4.716990566 and -4.716990566.Subproblem 1
x + -5.5 = 4.716990566 Simplifying x + -5.5 = 4.716990566 Reorder the terms: -5.5 + x = 4.716990566 Solving -5.5 + x = 4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.716990566 + 5.5 x = 4.716990566 + 5.5 Combine like terms: 4.716990566 + 5.5 = 10.216990566 x = 10.216990566 Simplifying x = 10.216990566Subproblem 2
x + -5.5 = -4.716990566 Simplifying x + -5.5 = -4.716990566 Reorder the terms: -5.5 + x = -4.716990566 Solving -5.5 + x = -4.716990566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -4.716990566 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.716990566 + 5.5 x = -4.716990566 + 5.5 Combine like terms: -4.716990566 + 5.5 = 0.783009434 x = 0.783009434 Simplifying x = 0.783009434Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.216990566, 0.783009434}Solution
x = {10.216990566, 0.783009434}
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