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Simplifying -22x + 2x2 = 156 Solving -22x + 2x2 = 156 Solving for variable 'x'. Reorder the terms: -156 + -22x + 2x2 = 156 + -156 Combine like terms: 156 + -156 = 0 -156 + -22x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-78 + -11x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-78 + -11x + x2)' equal to zero and attempt to solve: Simplifying -78 + -11x + x2 = 0 Solving -78 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '78' to each side of the equation. -78 + -11x + 78 + x2 = 0 + 78 Reorder the terms: -78 + 78 + -11x + x2 = 0 + 78 Combine like terms: -78 + 78 = 0 0 + -11x + x2 = 0 + 78 -11x + x2 = 0 + 78 Combine like terms: 0 + 78 = 78 -11x + x2 = 78 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 = 78 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 78 + 30.25 Combine like terms: 78 + 30.25 = 108.25 30.25 + -11x + x2 = 108.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 108.25 Calculate the square root of the right side: 10.404326023 Break this problem into two subproblems by setting (x + -5.5) equal to 10.404326023 and -10.404326023.Subproblem 1
x + -5.5 = 10.404326023 Simplifying x + -5.5 = 10.404326023 Reorder the terms: -5.5 + x = 10.404326023 Solving -5.5 + x = 10.404326023 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 = 10.404326023 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 10.404326023 + 5.5 x = 10.404326023 + 5.5 Combine like terms: 10.404326023 + 5.5 = 15.904326023 x = 15.904326023 Simplifying x = 15.904326023Subproblem 2
x + -5.5 = -10.404326023 Simplifying x + -5.5 = -10.404326023 Reorder the terms: -5.5 + x = -10.404326023 Solving -5.5 + x = -10.404326023 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 = -10.404326023 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -10.404326023 + 5.5 x = -10.404326023 + 5.5 Combine like terms: -10.404326023 + 5.5 = -4.904326023 x = -4.904326023 Simplifying x = -4.904326023Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.904326023, -4.904326023}Solution
x = {15.904326023, -4.904326023}
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