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Simplifying 18x2 + 26x + -22 = 0 Reorder the terms: -22 + 26x + 18x2 = 0 Solving -22 + 26x + 18x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-11 + 13x + 9x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-11 + 13x + 9x2)' equal to zero and attempt to solve: Simplifying -11 + 13x + 9x2 = 0 Solving -11 + 13x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -1.222222222 + 1.444444444x + x2 = 0 Move the constant term to the right: Add '1.222222222' to each side of the equation. -1.222222222 + 1.444444444x + 1.222222222 + x2 = 0 + 1.222222222 Reorder the terms: -1.222222222 + 1.222222222 + 1.444444444x + x2 = 0 + 1.222222222 Combine like terms: -1.222222222 + 1.222222222 = 0.000000000 0.000000000 + 1.444444444x + x2 = 0 + 1.222222222 1.444444444x + x2 = 0 + 1.222222222 Combine like terms: 0 + 1.222222222 = 1.222222222 1.444444444x + x2 = 1.222222222 The x term is 1.444444444x. Take half its coefficient (0.722222222). Square it (0.5216049380) and add it to both sides. Add '0.5216049380' to each side of the equation. 1.444444444x + 0.5216049380 + x2 = 1.222222222 + 0.5216049380 Reorder the terms: 0.5216049380 + 1.444444444x + x2 = 1.222222222 + 0.5216049380 Combine like terms: 1.222222222 + 0.5216049380 = 1.74382716 0.5216049380 + 1.444444444x + x2 = 1.74382716 Factor a perfect square on the left side: (x + 0.722222222)(x + 0.722222222) = 1.74382716 Calculate the square root of the right side: 1.32054048 Break this problem into two subproblems by setting (x + 0.722222222) equal to 1.32054048 and -1.32054048.Subproblem 1
x + 0.722222222 = 1.32054048 Simplifying x + 0.722222222 = 1.32054048 Reorder the terms: 0.722222222 + x = 1.32054048 Solving 0.722222222 + x = 1.32054048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = 1.32054048 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = 1.32054048 + -0.722222222 x = 1.32054048 + -0.722222222 Combine like terms: 1.32054048 + -0.722222222 = 0.598318258 x = 0.598318258 Simplifying x = 0.598318258Subproblem 2
x + 0.722222222 = -1.32054048 Simplifying x + 0.722222222 = -1.32054048 Reorder the terms: 0.722222222 + x = -1.32054048 Solving 0.722222222 + x = -1.32054048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.722222222' to each side of the equation. 0.722222222 + -0.722222222 + x = -1.32054048 + -0.722222222 Combine like terms: 0.722222222 + -0.722222222 = 0.000000000 0.000000000 + x = -1.32054048 + -0.722222222 x = -1.32054048 + -0.722222222 Combine like terms: -1.32054048 + -0.722222222 = -2.042762702 x = -2.042762702 Simplifying x = -2.042762702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.598318258, -2.042762702}Solution
x = {0.598318258, -2.042762702}
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