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Simplifying 310x2 + -500x + 200 = 0 Reorder the terms: 200 + -500x + 310x2 = 0 Solving 200 + -500x + 310x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(20 + -50x + 31x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(20 + -50x + 31x2)' equal to zero and attempt to solve: Simplifying 20 + -50x + 31x2 = 0 Solving 20 + -50x + 31x2 = 0 Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. 0.6451612903 + -1.612903226x + x2 = 0 Move the constant term to the right: Add '-0.6451612903' to each side of the equation. 0.6451612903 + -1.612903226x + -0.6451612903 + x2 = 0 + -0.6451612903 Reorder the terms: 0.6451612903 + -0.6451612903 + -1.612903226x + x2 = 0 + -0.6451612903 Combine like terms: 0.6451612903 + -0.6451612903 = 0.0000000000 0.0000000000 + -1.612903226x + x2 = 0 + -0.6451612903 -1.612903226x + x2 = 0 + -0.6451612903 Combine like terms: 0 + -0.6451612903 = -0.6451612903 -1.612903226x + x2 = -0.6451612903 The x term is -1.612903226x. Take half its coefficient (-0.806451613). Square it (0.6503642041) and add it to both sides. Add '0.6503642041' to each side of the equation. -1.612903226x + 0.6503642041 + x2 = -0.6451612903 + 0.6503642041 Reorder the terms: 0.6503642041 + -1.612903226x + x2 = -0.6451612903 + 0.6503642041 Combine like terms: -0.6451612903 + 0.6503642041 = 0.0052029138 0.6503642041 + -1.612903226x + x2 = 0.0052029138 Factor a perfect square on the left side: (x + -0.806451613)(x + -0.806451613) = 0.0052029138 Calculate the square root of the right side: 0.072131226 Break this problem into two subproblems by setting (x + -0.806451613) equal to 0.072131226 and -0.072131226.Subproblem 1
x + -0.806451613 = 0.072131226 Simplifying x + -0.806451613 = 0.072131226 Reorder the terms: -0.806451613 + x = 0.072131226 Solving -0.806451613 + x = 0.072131226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.806451613' to each side of the equation. -0.806451613 + 0.806451613 + x = 0.072131226 + 0.806451613 Combine like terms: -0.806451613 + 0.806451613 = 0.000000000 0.000000000 + x = 0.072131226 + 0.806451613 x = 0.072131226 + 0.806451613 Combine like terms: 0.072131226 + 0.806451613 = 0.878582839 x = 0.878582839 Simplifying x = 0.878582839Subproblem 2
x + -0.806451613 = -0.072131226 Simplifying x + -0.806451613 = -0.072131226 Reorder the terms: -0.806451613 + x = -0.072131226 Solving -0.806451613 + x = -0.072131226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.806451613' to each side of the equation. -0.806451613 + 0.806451613 + x = -0.072131226 + 0.806451613 Combine like terms: -0.806451613 + 0.806451613 = 0.000000000 0.000000000 + x = -0.072131226 + 0.806451613 x = -0.072131226 + 0.806451613 Combine like terms: -0.072131226 + 0.806451613 = 0.734320387 x = 0.734320387 Simplifying x = 0.734320387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.878582839, 0.734320387}Solution
x = {0.878582839, 0.734320387}
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