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Simplifying 150x2 + -170x + -26 = 0 Reorder the terms: -26 + -170x + 150x2 = 0 Solving -26 + -170x + 150x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + -85x + 75x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + -85x + 75x2)' equal to zero and attempt to solve: Simplifying -13 + -85x + 75x2 = 0 Solving -13 + -85x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. -0.1733333333 + -1.133333333x + x2 = 0 Move the constant term to the right: Add '0.1733333333' to each side of the equation. -0.1733333333 + -1.133333333x + 0.1733333333 + x2 = 0 + 0.1733333333 Reorder the terms: -0.1733333333 + 0.1733333333 + -1.133333333x + x2 = 0 + 0.1733333333 Combine like terms: -0.1733333333 + 0.1733333333 = 0.0000000000 0.0000000000 + -1.133333333x + x2 = 0 + 0.1733333333 -1.133333333x + x2 = 0 + 0.1733333333 Combine like terms: 0 + 0.1733333333 = 0.1733333333 -1.133333333x + x2 = 0.1733333333 The x term is -1.133333333x. Take half its coefficient (-0.5666666665). Square it (0.3211111109) and add it to both sides. Add '0.3211111109' to each side of the equation. -1.133333333x + 0.3211111109 + x2 = 0.1733333333 + 0.3211111109 Reorder the terms: 0.3211111109 + -1.133333333x + x2 = 0.1733333333 + 0.3211111109 Combine like terms: 0.1733333333 + 0.3211111109 = 0.4944444442 0.3211111109 + -1.133333333x + x2 = 0.4944444442 Factor a perfect square on the left side: (x + -0.5666666665)(x + -0.5666666665) = 0.4944444442 Calculate the square root of the right side: 0.703167437 Break this problem into two subproblems by setting (x + -0.5666666665) equal to 0.703167437 and -0.703167437.Subproblem 1
x + -0.5666666665 = 0.703167437 Simplifying x + -0.5666666665 = 0.703167437 Reorder the terms: -0.5666666665 + x = 0.703167437 Solving -0.5666666665 + x = 0.703167437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5666666665' to each side of the equation. -0.5666666665 + 0.5666666665 + x = 0.703167437 + 0.5666666665 Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000 0.0000000000 + x = 0.703167437 + 0.5666666665 x = 0.703167437 + 0.5666666665 Combine like terms: 0.703167437 + 0.5666666665 = 1.2698341035 x = 1.2698341035 Simplifying x = 1.2698341035Subproblem 2
x + -0.5666666665 = -0.703167437 Simplifying x + -0.5666666665 = -0.703167437 Reorder the terms: -0.5666666665 + x = -0.703167437 Solving -0.5666666665 + x = -0.703167437 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5666666665' to each side of the equation. -0.5666666665 + 0.5666666665 + x = -0.703167437 + 0.5666666665 Combine like terms: -0.5666666665 + 0.5666666665 = 0.0000000000 0.0000000000 + x = -0.703167437 + 0.5666666665 x = -0.703167437 + 0.5666666665 Combine like terms: -0.703167437 + 0.5666666665 = -0.1365007705 x = -0.1365007705 Simplifying x = -0.1365007705Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2698341035, -0.1365007705}Solution
x = {1.2698341035, -0.1365007705}
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