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Simplifying 60x2 + 86x + 16 = 0 Reorder the terms: 16 + 86x + 60x2 = 0 Solving 16 + 86x + 60x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(8 + 43x + 30x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + 43x + 30x2)' equal to zero and attempt to solve: Simplifying 8 + 43x + 30x2 = 0 Solving 8 + 43x + 30x2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.2666666667 + 1.433333333x + x2 = 0.0 Move the constant term to the right: Add '-0.2666666667' to each side of the equation. 0.2666666667 + 1.433333333x + -0.2666666667 + x2 = 0.0 + -0.2666666667 Reorder the terms: 0.2666666667 + -0.2666666667 + 1.433333333x + x2 = 0.0 + -0.2666666667 Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000 0.0000000000 + 1.433333333x + x2 = 0.0 + -0.2666666667 1.433333333x + x2 = 0.0 + -0.2666666667 Combine like terms: 0.0 + -0.2666666667 = -0.2666666667 1.433333333x + x2 = -0.2666666667 The x term is 1.433333333x. Take half its coefficient (0.7166666665). Square it (0.5136111109) and add it to both sides. Add '0.5136111109' to each side of the equation. 1.433333333x + 0.5136111109 + x2 = -0.2666666667 + 0.5136111109 Reorder the terms: 0.5136111109 + 1.433333333x + x2 = -0.2666666667 + 0.5136111109 Combine like terms: -0.2666666667 + 0.5136111109 = 0.2469444442 0.5136111109 + 1.433333333x + x2 = 0.2469444442 Factor a perfect square on the left side: (x + 0.7166666665)(x + 0.7166666665) = 0.2469444442 Calculate the square root of the right side: 0.49693505 Break this problem into two subproblems by setting (x + 0.7166666665) equal to 0.49693505 and -0.49693505.Subproblem 1
x + 0.7166666665 = 0.49693505 Simplifying x + 0.7166666665 = 0.49693505 Reorder the terms: 0.7166666665 + x = 0.49693505 Solving 0.7166666665 + x = 0.49693505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7166666665' to each side of the equation. 0.7166666665 + -0.7166666665 + x = 0.49693505 + -0.7166666665 Combine like terms: 0.7166666665 + -0.7166666665 = 0.0000000000 0.0000000000 + x = 0.49693505 + -0.7166666665 x = 0.49693505 + -0.7166666665 Combine like terms: 0.49693505 + -0.7166666665 = -0.2197316165 x = -0.2197316165 Simplifying x = -0.2197316165Subproblem 2
x + 0.7166666665 = -0.49693505 Simplifying x + 0.7166666665 = -0.49693505 Reorder the terms: 0.7166666665 + x = -0.49693505 Solving 0.7166666665 + x = -0.49693505 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7166666665' to each side of the equation. 0.7166666665 + -0.7166666665 + x = -0.49693505 + -0.7166666665 Combine like terms: 0.7166666665 + -0.7166666665 = 0.0000000000 0.0000000000 + x = -0.49693505 + -0.7166666665 x = -0.49693505 + -0.7166666665 Combine like terms: -0.49693505 + -0.7166666665 = -1.2136017165 x = -1.2136017165 Simplifying x = -1.2136017165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2197316165, -1.2136017165}Solution
x = {-0.2197316165, -1.2136017165}
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