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Simplifying 21x2 + 110x + -3025 = 0 Reorder the terms: -3025 + 110x + 21x2 = 0 Solving -3025 + 110x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -144.047619 + 5.238095238x + x2 = 0 Move the constant term to the right: Add '144.047619' to each side of the equation. -144.047619 + 5.238095238x + 144.047619 + x2 = 0 + 144.047619 Reorder the terms: -144.047619 + 144.047619 + 5.238095238x + x2 = 0 + 144.047619 Combine like terms: -144.047619 + 144.047619 = 0.000000 0.000000 + 5.238095238x + x2 = 0 + 144.047619 5.238095238x + x2 = 0 + 144.047619 Combine like terms: 0 + 144.047619 = 144.047619 5.238095238x + x2 = 144.047619 The x term is 5.238095238x. Take half its coefficient (2.619047619). Square it (6.859410431) and add it to both sides. Add '6.859410431' to each side of the equation. 5.238095238x + 6.859410431 + x2 = 144.047619 + 6.859410431 Reorder the terms: 6.859410431 + 5.238095238x + x2 = 144.047619 + 6.859410431 Combine like terms: 144.047619 + 6.859410431 = 150.907029431 6.859410431 + 5.238095238x + x2 = 150.907029431 Factor a perfect square on the left side: (x + 2.619047619)(x + 2.619047619) = 150.907029431 Calculate the square root of the right side: 12.284422226 Break this problem into two subproblems by setting (x + 2.619047619) equal to 12.284422226 and -12.284422226.Subproblem 1
x + 2.619047619 = 12.284422226 Simplifying x + 2.619047619 = 12.284422226 Reorder the terms: 2.619047619 + x = 12.284422226 Solving 2.619047619 + x = 12.284422226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.619047619' to each side of the equation. 2.619047619 + -2.619047619 + x = 12.284422226 + -2.619047619 Combine like terms: 2.619047619 + -2.619047619 = 0.000000000 0.000000000 + x = 12.284422226 + -2.619047619 x = 12.284422226 + -2.619047619 Combine like terms: 12.284422226 + -2.619047619 = 9.665374607 x = 9.665374607 Simplifying x = 9.665374607Subproblem 2
x + 2.619047619 = -12.284422226 Simplifying x + 2.619047619 = -12.284422226 Reorder the terms: 2.619047619 + x = -12.284422226 Solving 2.619047619 + x = -12.284422226 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.619047619' to each side of the equation. 2.619047619 + -2.619047619 + x = -12.284422226 + -2.619047619 Combine like terms: 2.619047619 + -2.619047619 = 0.000000000 0.000000000 + x = -12.284422226 + -2.619047619 x = -12.284422226 + -2.619047619 Combine like terms: -12.284422226 + -2.619047619 = -14.903469845 x = -14.903469845 Simplifying x = -14.903469845Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.665374607, -14.903469845}
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