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Simplifying 42x2 + -476x + -2460 = 0 Reorder the terms: -2460 + -476x + 42x2 = 0 Solving -2460 + -476x + 42x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1230 + -238x + 21x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1230 + -238x + 21x2)' equal to zero and attempt to solve: Simplifying -1230 + -238x + 21x2 = 0 Solving -1230 + -238x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -58.57142857 + -11.33333333x + x2 = 0 Move the constant term to the right: Add '58.57142857' to each side of the equation. -58.57142857 + -11.33333333x + 58.57142857 + x2 = 0 + 58.57142857 Reorder the terms: -58.57142857 + 58.57142857 + -11.33333333x + x2 = 0 + 58.57142857 Combine like terms: -58.57142857 + 58.57142857 = 0.00000000 0.00000000 + -11.33333333x + x2 = 0 + 58.57142857 -11.33333333x + x2 = 0 + 58.57142857 Combine like terms: 0 + 58.57142857 = 58.57142857 -11.33333333x + x2 = 58.57142857 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 = 58.57142857 + 32.11111109 Reorder the terms: 32.11111109 + -11.33333333x + x2 = 58.57142857 + 32.11111109 Combine like terms: 58.57142857 + 32.11111109 = 90.68253966 32.11111109 + -11.33333333x + x2 = 90.68253966 Factor a perfect square on the left side: (x + -5.666666665)(x + -5.666666665) = 90.68253966 Calculate the square root of the right side: 9.522738034 Break this problem into two subproblems by setting (x + -5.666666665) equal to 9.522738034 and -9.522738034.Subproblem 1
x + -5.666666665 = 9.522738034 Simplifying x + -5.666666665 = 9.522738034 Reorder the terms: -5.666666665 + x = 9.522738034 Solving -5.666666665 + x = 9.522738034 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 = 9.522738034 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = 9.522738034 + 5.666666665 x = 9.522738034 + 5.666666665 Combine like terms: 9.522738034 + 5.666666665 = 15.189404699 x = 15.189404699 Simplifying x = 15.189404699Subproblem 2
x + -5.666666665 = -9.522738034 Simplifying x + -5.666666665 = -9.522738034 Reorder the terms: -5.666666665 + x = -9.522738034 Solving -5.666666665 + x = -9.522738034 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 = -9.522738034 + 5.666666665 Combine like terms: -5.666666665 + 5.666666665 = 0.000000000 0.000000000 + x = -9.522738034 + 5.666666665 x = -9.522738034 + 5.666666665 Combine like terms: -9.522738034 + 5.666666665 = -3.856071369 x = -3.856071369 Simplifying x = -3.856071369Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.189404699, -3.856071369}Solution
x = {15.189404699, -3.856071369}
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