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Simplifying 2x2 + -35x + 10 = 0 Reorder the terms: 10 + -35x + 2x2 = 0 Solving 10 + -35x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + -17.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -17.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -17.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -17.5x + x2 = 0 + -5 -17.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -17.5x + x2 = -5 The x term is -17.5x. Take half its coefficient (-8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. -17.5x + 76.5625 + x2 = -5 + 76.5625 Reorder the terms: 76.5625 + -17.5x + x2 = -5 + 76.5625 Combine like terms: -5 + 76.5625 = 71.5625 76.5625 + -17.5x + x2 = 71.5625 Factor a perfect square on the left side: (x + -8.75)(x + -8.75) = 71.5625 Calculate the square root of the right side: 8.459462158 Break this problem into two subproblems by setting (x + -8.75) equal to 8.459462158 and -8.459462158.Subproblem 1
x + -8.75 = 8.459462158 Simplifying x + -8.75 = 8.459462158 Reorder the terms: -8.75 + x = 8.459462158 Solving -8.75 + x = 8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = 8.459462158 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = 8.459462158 + 8.75 x = 8.459462158 + 8.75 Combine like terms: 8.459462158 + 8.75 = 17.209462158 x = 17.209462158 Simplifying x = 17.209462158Subproblem 2
x + -8.75 = -8.459462158 Simplifying x + -8.75 = -8.459462158 Reorder the terms: -8.75 + x = -8.459462158 Solving -8.75 + x = -8.459462158 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.75' to each side of the equation. -8.75 + 8.75 + x = -8.459462158 + 8.75 Combine like terms: -8.75 + 8.75 = 0.00 0.00 + x = -8.459462158 + 8.75 x = -8.459462158 + 8.75 Combine like terms: -8.459462158 + 8.75 = 0.290537842 x = 0.290537842 Simplifying x = 0.290537842Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.209462158, 0.290537842}
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