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Simplifying 2x2 + -18x + 22 = 0 Reorder the terms: 22 + -18x + 2x2 = 0 Solving 22 + -18x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -9x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -9x + x2)' equal to zero and attempt to solve: Simplifying 11 + -9x + x2 = 0 Solving 11 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-11' to each side of the equation. 11 + -9x + -11 + x2 = 0 + -11 Reorder the terms: 11 + -11 + -9x + x2 = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -9x + x2 = 0 + -11 -9x + x2 = 0 + -11 Combine like terms: 0 + -11 = -11 -9x + x2 = -11 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = -11 + 20.25 Reorder the terms: 20.25 + -9x + x2 = -11 + 20.25 Combine like terms: -11 + 20.25 = 9.25 20.25 + -9x + x2 = 9.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 9.25 Calculate the square root of the right side: 3.041381265 Break this problem into two subproblems by setting (x + -4.5) equal to 3.041381265 and -3.041381265.Subproblem 1
x + -4.5 = 3.041381265 Simplifying x + -4.5 = 3.041381265 Reorder the terms: -4.5 + x = 3.041381265 Solving -4.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.041381265 + 4.5 x = 3.041381265 + 4.5 Combine like terms: 3.041381265 + 4.5 = 7.541381265 x = 7.541381265 Simplifying x = 7.541381265Subproblem 2
x + -4.5 = -3.041381265 Simplifying x + -4.5 = -3.041381265 Reorder the terms: -4.5 + x = -3.041381265 Solving -4.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.041381265 + 4.5 x = -3.041381265 + 4.5 Combine like terms: -3.041381265 + 4.5 = 1.458618735 x = 1.458618735 Simplifying x = 1.458618735Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.541381265, 1.458618735}Solution
x = {7.541381265, 1.458618735}
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