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Simplifying 0 = 14.113x2 + -1579.39x + -2635.875 Reorder the terms: 0 = -2635.875 + -1579.39x + 14.113x2 Solving 0 = -2635.875 + -1579.39x + 14.113x2 Solving for variable 'x'. Combine like terms: 0 + 2635.875 = 2635.875 2635.875 + 1579.39x + -14.113x2 = -2635.875 + -1579.39x + 14.113x2 + 2635.875 + 1579.39x + -14.113x2 Reorder the terms: 2635.875 + 1579.39x + -14.113x2 = -2635.875 + 2635.875 + -1579.39x + 1579.39x + 14.113x2 + -14.113x2 Combine like terms: -2635.875 + 2635.875 = 0.000 2635.875 + 1579.39x + -14.113x2 = 0.000 + -1579.39x + 1579.39x + 14.113x2 + -14.113x2 2635.875 + 1579.39x + -14.113x2 = -1579.39x + 1579.39x + 14.113x2 + -14.113x2 Combine like terms: -1579.39x + 1579.39x = 0.00 2635.875 + 1579.39x + -14.113x2 = 0.00 + 14.113x2 + -14.113x2 2635.875 + 1579.39x + -14.113x2 = 14.113x2 + -14.113x2 Combine like terms: 14.113x2 + -14.113x2 = 0.000 2635.875 + 1579.39x + -14.113x2 = 0.000 Begin completing the square. Divide all terms by -14.113 the coefficient of the squared term: Divide each side by '-14.113'. -186.7692907 + -111.9102955x + x2 = 0 Move the constant term to the right: Add '186.7692907' to each side of the equation. -186.7692907 + -111.9102955x + 186.7692907 + x2 = 0 + 186.7692907 Reorder the terms: -186.7692907 + 186.7692907 + -111.9102955x + x2 = 0 + 186.7692907 Combine like terms: -186.7692907 + 186.7692907 = 0.0000000 0.0000000 + -111.9102955x + x2 = 0 + 186.7692907 -111.9102955x + x2 = 0 + 186.7692907 Combine like terms: 0 + 186.7692907 = 186.7692907 -111.9102955x + x2 = 186.7692907 The x term is -111.9102955x. Take half its coefficient (-55.95514775). Square it (3130.978560) and add it to both sides. Add '3130.978560' to each side of the equation. -111.9102955x + 3130.978560 + x2 = 186.7692907 + 3130.978560 Reorder the terms: 3130.978560 + -111.9102955x + x2 = 186.7692907 + 3130.978560 Combine like terms: 186.7692907 + 3130.978560 = 3317.7478507 3130.978560 + -111.9102955x + x2 = 3317.7478507 Factor a perfect square on the left side: (x + -55.95514775)(x + -55.95514775) = 3317.7478507 Calculate the square root of the right side: 57.599894537 Break this problem into two subproblems by setting (x + -55.95514775) equal to 57.599894537 and -57.599894537.Subproblem 1
x + -55.95514775 = 57.599894537 Simplifying x + -55.95514775 = 57.599894537 Reorder the terms: -55.95514775 + x = 57.599894537 Solving -55.95514775 + x = 57.599894537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.95514775' to each side of the equation. -55.95514775 + 55.95514775 + x = 57.599894537 + 55.95514775 Combine like terms: -55.95514775 + 55.95514775 = 0.00000000 0.00000000 + x = 57.599894537 + 55.95514775 x = 57.599894537 + 55.95514775 Combine like terms: 57.599894537 + 55.95514775 = 113.555042287 x = 113.555042287 Simplifying x = 113.555042287Subproblem 2
x + -55.95514775 = -57.599894537 Simplifying x + -55.95514775 = -57.599894537 Reorder the terms: -55.95514775 + x = -57.599894537 Solving -55.95514775 + x = -57.599894537 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55.95514775' to each side of the equation. -55.95514775 + 55.95514775 + x = -57.599894537 + 55.95514775 Combine like terms: -55.95514775 + 55.95514775 = 0.00000000 0.00000000 + x = -57.599894537 + 55.95514775 x = -57.599894537 + 55.95514775 Combine like terms: -57.599894537 + 55.95514775 = -1.644746787 x = -1.644746787 Simplifying x = -1.644746787Solution
The solution to the problem is based on the solutions from the subproblems. x = {113.555042287, -1.644746787}
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