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Simplifying x2 + -35x + 70 = 0 Reorder the terms: 70 + -35x + x2 = 0 Solving 70 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -35x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -35x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -35x + x2 = 0 + -70 -35x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -35x + x2 = -70 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 = -70 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -70 + 306.25 Combine like terms: -70 + 306.25 = 236.25 306.25 + -35x + x2 = 236.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 236.25 Calculate the square root of the right side: 15.370426149 Break this problem into two subproblems by setting (x + -17.5) equal to 15.370426149 and -15.370426149.Subproblem 1
x + -17.5 = 15.370426149 Simplifying x + -17.5 = 15.370426149 Reorder the terms: -17.5 + x = 15.370426149 Solving -17.5 + x = 15.370426149 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 = 15.370426149 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 15.370426149 + 17.5 x = 15.370426149 + 17.5 Combine like terms: 15.370426149 + 17.5 = 32.870426149 x = 32.870426149 Simplifying x = 32.870426149Subproblem 2
x + -17.5 = -15.370426149 Simplifying x + -17.5 = -15.370426149 Reorder the terms: -17.5 + x = -15.370426149 Solving -17.5 + x = -15.370426149 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 = -15.370426149 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -15.370426149 + 17.5 x = -15.370426149 + 17.5 Combine like terms: -15.370426149 + 17.5 = 2.129573851 x = 2.129573851 Simplifying x = 2.129573851Solution
The solution to the problem is based on the solutions from the subproblems. x = {32.870426149, 2.129573851}
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