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Simplifying x2 + -70x + 109 = 0 Reorder the terms: 109 + -70x + x2 = 0 Solving 109 + -70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-109' to each side of the equation. 109 + -70x + -109 + x2 = 0 + -109 Reorder the terms: 109 + -109 + -70x + x2 = 0 + -109 Combine like terms: 109 + -109 = 0 0 + -70x + x2 = 0 + -109 -70x + x2 = 0 + -109 Combine like terms: 0 + -109 = -109 -70x + x2 = -109 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 = -109 + 1225 Reorder the terms: 1225 + -70x + x2 = -109 + 1225 Combine like terms: -109 + 1225 = 1116 1225 + -70x + x2 = 1116 Factor a perfect square on the left side: (x + -35)(x + -35) = 1116 Calculate the square root of the right side: 33.406586177 Break this problem into two subproblems by setting (x + -35) equal to 33.406586177 and -33.406586177.Subproblem 1
x + -35 = 33.406586177 Simplifying x + -35 = 33.406586177 Reorder the terms: -35 + x = 33.406586177 Solving -35 + x = 33.406586177 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 = 33.406586177 + 35 Combine like terms: -35 + 35 = 0 0 + x = 33.406586177 + 35 x = 33.406586177 + 35 Combine like terms: 33.406586177 + 35 = 68.406586177 x = 68.406586177 Simplifying x = 68.406586177Subproblem 2
x + -35 = -33.406586177 Simplifying x + -35 = -33.406586177 Reorder the terms: -35 + x = -33.406586177 Solving -35 + x = -33.406586177 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 = -33.406586177 + 35 Combine like terms: -35 + 35 = 0 0 + x = -33.406586177 + 35 x = -33.406586177 + 35 Combine like terms: -33.406586177 + 35 = 1.593413823 x = 1.593413823 Simplifying x = 1.593413823Solution
The solution to the problem is based on the solutions from the subproblems. x = {68.406586177, 1.593413823}
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