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Simplifying 2x2 + -70x = 17 Reorder the terms: -70x + 2x2 = 17 Solving -70x + 2x2 = 17 Solving for variable 'x'. Reorder the terms: -17 + -70x + 2x2 = 17 + -17 Combine like terms: 17 + -17 = 0 -17 + -70x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -8.5 + -35x + x2 = 0 Move the constant term to the right: Add '8.5' to each side of the equation. -8.5 + -35x + 8.5 + x2 = 0 + 8.5 Reorder the terms: -8.5 + 8.5 + -35x + x2 = 0 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + -35x + x2 = 0 + 8.5 -35x + x2 = 0 + 8.5 Combine like terms: 0 + 8.5 = 8.5 -35x + x2 = 8.5 The x term is -35x. Take half its coefficient (-17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. -35x + 306.25 + x2 = 8.5 + 306.25 Reorder the terms: 306.25 + -35x + x2 = 8.5 + 306.25 Combine like terms: 8.5 + 306.25 = 314.75 306.25 + -35x + x2 = 314.75 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 314.75 Calculate the square root of the right side: 17.741194999 Break this problem into two subproblems by setting (x + -17.5) equal to 17.741194999 and -17.741194999.Subproblem 1
x + -17.5 = 17.741194999 Simplifying x + -17.5 = 17.741194999 Reorder the terms: -17.5 + x = 17.741194999 Solving -17.5 + x = 17.741194999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 17.741194999 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 17.741194999 + 17.5 x = 17.741194999 + 17.5 Combine like terms: 17.741194999 + 17.5 = 35.241194999 x = 35.241194999 Simplifying x = 35.241194999Subproblem 2
x + -17.5 = -17.741194999 Simplifying x + -17.5 = -17.741194999 Reorder the terms: -17.5 + x = -17.741194999 Solving -17.5 + x = -17.741194999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -17.741194999 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -17.741194999 + 17.5 x = -17.741194999 + 17.5 Combine like terms: -17.741194999 + 17.5 = -0.241194999 x = -0.241194999 Simplifying x = -0.241194999Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.241194999, -0.241194999}
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