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Simplifying 42x2 + -476x + -2494 = 0 Reorder the terms: -2494 + -476x + 42x2 = 0 Solving -2494 + -476x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1247 + -238x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1247 + -238x + 21x2)' equal to zero and attempt to solve: Simplifying -1247 + -238x + 21x2 = 0 Solving -1247 + -238x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -59.38095238 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '59.38095238' to each side of the equation. -59.38095238 + -11.33333333x + 59.38095238 + x2 = 0 + 59.38095238 Reorder the terms: -59.38095238 + 59.38095238 + -11.33333333x + x2 = 0 + 59.38095238 Combine like terms: -59.38095238 + 59.38095238 = 0.00000000 0.00000000 + -11.33333333x + x2 = 0 + 59.38095238 -11.33333333x + x2 = 0 + 59.38095238 Combine like terms: 0 + 59.38095238 = 59.38095238 -11.33333333x + x2 = 59.38095238 The x term is -11.33333333x. Take half its coefficient (-5.666666665). Square it (32.11111109) and add it to both sides. Add '32.11111109' to each side of the equation. -11.33333333x + 32.11111109 + x2 = 59.38095238 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = 59.38095238 + 32.11111109 Combine like terms: 59.38095238 + 32.11111109 = 91.49206347 32.11111109 + -11.33333333x + x2 = 91.49206347 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 91.49206347 Calculate the square root of the right side: 9.565148377 Break this problem into two subproblems by setting (x + -5.666666665) equal to 9.565148377 and -9.565148377.Subproblem 1
x + -5.666666665 = 9.565148377 Simplifying x + -5.666666665 = 9.565148377 Reorder the terms: -5.666666665 + x = 9.565148377 Solving -5.666666665 + x = 9.565148377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = 9.565148377 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 9.565148377 + 5.666666665 x = 9.565148377 + 5.666666665 Combine like terms: 9.565148377 + 5.666666665 = 15.231815042 x = 15.231815042 Simplifying x = 15.231815042Subproblem 2
x + -5.666666665 = -9.565148377 Simplifying x + -5.666666665 = -9.565148377 Reorder the terms: -5.666666665 + x = -9.565148377 Solving -5.666666665 + x = -9.565148377 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.666666665' to each side of the equation. -5.666666665 + 5.666666665 + x = -9.565148377 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -9.565148377 + 5.666666665 x = -9.565148377 + 5.666666665 Combine like terms: -9.565148377 + 5.666666665 = -3.898481712 x = -3.898481712 Simplifying x = -3.898481712Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.231815042, -3.898481712}Solution
x = {15.231815042, -3.898481712}
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