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Simplifying 90x2 + -120x + -56 = 0 Reorder the terms: -56 + -120x + 90x2 = 0 Solving -56 + -120x + 90x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-28 + -60x + 45x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-28 + -60x + 45x2)' equal to zero and attempt to solve: Simplifying -28 + -60x + 45x2 = 0 Solving -28 + -60x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.6222222222 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.6222222222' to each side of the equation. -0.6222222222 + -1.333333333x + 0.6222222222 + x2 = 0 + 0.6222222222 Reorder the terms: -0.6222222222 + 0.6222222222 + -1.333333333x + x2 = 0 + 0.6222222222 Combine like terms: -0.6222222222 + 0.6222222222 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.6222222222 -1.333333333x + x2 = 0 + 0.6222222222 Combine like terms: 0 + 0.6222222222 = 0.6222222222 -1.333333333x + x2 = 0.6222222222 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 0.6222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.6222222222 + 0.4444444442 Combine like terms: 0.6222222222 + 0.4444444442 = 1.0666666664 0.4444444442 + -1.333333333x + x2 = 1.0666666664 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.0666666664 Calculate the square root of the right side: 1.032795559 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.032795559 and -1.032795559.Subproblem 1
x + -0.6666666665 = 1.032795559 Simplifying x + -0.6666666665 = 1.032795559 Reorder the terms: -0.6666666665 + x = 1.032795559 Solving -0.6666666665 + x = 1.032795559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 1.032795559 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.032795559 + 0.6666666665 x = 1.032795559 + 0.6666666665 Combine like terms: 1.032795559 + 0.6666666665 = 1.6994622255 x = 1.6994622255 Simplifying x = 1.6994622255Subproblem 2
x + -0.6666666665 = -1.032795559 Simplifying x + -0.6666666665 = -1.032795559 Reorder the terms: -0.6666666665 + x = -1.032795559 Solving -0.6666666665 + x = -1.032795559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -1.032795559 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.032795559 + 0.6666666665 x = -1.032795559 + 0.6666666665 Combine like terms: -1.032795559 + 0.6666666665 = -0.3661288925 x = -0.3661288925 Simplifying x = -0.3661288925Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6994622255, -0.3661288925}Solution
x = {1.6994622255, -0.3661288925}
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