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Simplifying 22x2 + -60x + 36 = 0 Reorder the terms: 36 + -60x + 22x2 = 0 Solving 36 + -60x + 22x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(18 + -30x + 11x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(18 + -30x + 11x2)' equal to zero and attempt to solve: Simplifying 18 + -30x + 11x2 = 0 Solving 18 + -30x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 1.636363636 + -2.727272727x + x2 = 0 Move the constant term to the right: Add '-1.636363636' to each side of the equation. 1.636363636 + -2.727272727x + -1.636363636 + x2 = 0 + -1.636363636 Reorder the terms: 1.636363636 + -1.636363636 + -2.727272727x + x2 = 0 + -1.636363636 Combine like terms: 1.636363636 + -1.636363636 = 0.000000000 0.000000000 + -2.727272727x + x2 = 0 + -1.636363636 -2.727272727x + x2 = 0 + -1.636363636 Combine like terms: 0 + -1.636363636 = -1.636363636 -2.727272727x + x2 = -1.636363636 The x term is -2.727272727x. Take half its coefficient (-1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. -2.727272727x + 1.859504133 + x2 = -1.636363636 + 1.859504133 Reorder the terms: 1.859504133 + -2.727272727x + x2 = -1.636363636 + 1.859504133 Combine like terms: -1.636363636 + 1.859504133 = 0.223140497 1.859504133 + -2.727272727x + x2 = 0.223140497 Factor a perfect square on the left side: (x + -1.363636364)(x + -1.363636364) = 0.223140497 Calculate the square root of the right side: 0.472377494 Break this problem into two subproblems by setting (x + -1.363636364) equal to 0.472377494 and -0.472377494.Subproblem 1
x + -1.363636364 = 0.472377494 Simplifying x + -1.363636364 = 0.472377494 Reorder the terms: -1.363636364 + x = 0.472377494 Solving -1.363636364 + x = 0.472377494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = 0.472377494 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = 0.472377494 + 1.363636364 x = 0.472377494 + 1.363636364 Combine like terms: 0.472377494 + 1.363636364 = 1.836013858 x = 1.836013858 Simplifying x = 1.836013858Subproblem 2
x + -1.363636364 = -0.472377494 Simplifying x + -1.363636364 = -0.472377494 Reorder the terms: -1.363636364 + x = -0.472377494 Solving -1.363636364 + x = -0.472377494 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.363636364' to each side of the equation. -1.363636364 + 1.363636364 + x = -0.472377494 + 1.363636364 Combine like terms: -1.363636364 + 1.363636364 = 0.000000000 0.000000000 + x = -0.472377494 + 1.363636364 x = -0.472377494 + 1.363636364 Combine like terms: -0.472377494 + 1.363636364 = 0.89125887 x = 0.89125887 Simplifying x = 0.89125887Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.836013858, 0.89125887}Solution
x = {1.836013858, 0.89125887}
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