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Simplifying x2 + -70x + 60 = 0 Reorder the terms: 60 + -70x + x2 = 0 Solving 60 + -70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -70x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -70x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -70x + x2 = 0 + -60 -70x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -70x + x2 = -60 The x term is -70x. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70x + 1225 + x2 = -60 + 1225 Reorder the terms: 1225 + -70x + x2 = -60 + 1225 Combine like terms: -60 + 1225 = 1165 1225 + -70x + x2 = 1165 Factor a perfect square on the left side: (x + -35)(x + -35) = 1165 Calculate the square root of the right side: 34.132096332 Break this problem into two subproblems by setting (x + -35) equal to 34.132096332 and -34.132096332.Subproblem 1
x + -35 = 34.132096332 Simplifying x + -35 = 34.132096332 Reorder the terms: -35 + x = 34.132096332 Solving -35 + x = 34.132096332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = 34.132096332 + 35 Combine like terms: -35 + 35 = 0 0 + x = 34.132096332 + 35 x = 34.132096332 + 35 Combine like terms: 34.132096332 + 35 = 69.132096332 x = 69.132096332 Simplifying x = 69.132096332Subproblem 2
x + -35 = -34.132096332 Simplifying x + -35 = -34.132096332 Reorder the terms: -35 + x = -34.132096332 Solving -35 + x = -34.132096332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + x = -34.132096332 + 35 Combine like terms: -35 + 35 = 0 0 + x = -34.132096332 + 35 x = -34.132096332 + 35 Combine like terms: -34.132096332 + 35 = 0.867903668 x = 0.867903668 Simplifying x = 0.867903668Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.132096332, 0.867903668}
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