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Simplifying -0.51x2 + 100x = 1700 Reorder the terms: 100x + -0.51x2 = 1700 Solving 100x + -0.51x2 = 1700 Solving for variable 'x'. Reorder the terms: -1700 + 100x + -0.51x2 = 1700 + -1700 Combine like terms: 1700 + -1700 = 0 -1700 + 100x + -0.51x2 = 0 Begin completing the square. Divide all terms by -0.51 the coefficient of the squared term: Divide each side by '-0.51'. 3333.333333 + -196.0784314x + x2 = 0 Move the constant term to the right: Add '-3333.333333' to each side of the equation. 3333.333333 + -196.0784314x + -3333.333333 + x2 = 0 + -3333.333333 Reorder the terms: 3333.333333 + -3333.333333 + -196.0784314x + x2 = 0 + -3333.333333 Combine like terms: 3333.333333 + -3333.333333 = 0.000000 0.000000 + -196.0784314x + x2 = 0 + -3333.333333 -196.0784314x + x2 = 0 + -3333.333333 Combine like terms: 0 + -3333.333333 = -3333.333333 -196.0784314x + x2 = -3333.333333 The x term is -196.0784314x. Take half its coefficient (-98.0392157). Square it (9611.687815) and add it to both sides. Add '9611.687815' to each side of the equation. -196.0784314x + 9611.687815 + x2 = -3333.333333 + 9611.687815 Reorder the terms: 9611.687815 + -196.0784314x + x2 = -3333.333333 + 9611.687815 Combine like terms: -3333.333333 + 9611.687815 = 6278.354482 9611.687815 + -196.0784314x + x2 = 6278.354482 Factor a perfect square on the left side: (x + -98.0392157)(x + -98.0392157) = 6278.354482 Calculate the square root of the right side: 79.236068062 Break this problem into two subproblems by setting (x + -98.0392157) equal to 79.236068062 and -79.236068062.Subproblem 1
x + -98.0392157 = 79.236068062 Simplifying x + -98.0392157 = 79.236068062 Reorder the terms: -98.0392157 + x = 79.236068062 Solving -98.0392157 + x = 79.236068062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.0392157' to each side of the equation. -98.0392157 + 98.0392157 + x = 79.236068062 + 98.0392157 Combine like terms: -98.0392157 + 98.0392157 = 0.0000000 0.0000000 + x = 79.236068062 + 98.0392157 x = 79.236068062 + 98.0392157 Combine like terms: 79.236068062 + 98.0392157 = 177.275283762 x = 177.275283762 Simplifying x = 177.275283762Subproblem 2
x + -98.0392157 = -79.236068062 Simplifying x + -98.0392157 = -79.236068062 Reorder the terms: -98.0392157 + x = -79.236068062 Solving -98.0392157 + x = -79.236068062 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '98.0392157' to each side of the equation. -98.0392157 + 98.0392157 + x = -79.236068062 + 98.0392157 Combine like terms: -98.0392157 + 98.0392157 = 0.0000000 0.0000000 + x = -79.236068062 + 98.0392157 x = -79.236068062 + 98.0392157 Combine like terms: -79.236068062 + 98.0392157 = 18.803147638 x = 18.803147638 Simplifying x = 18.803147638Solution
The solution to the problem is based on the solutions from the subproblems. x = {177.275283762, 18.803147638}
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