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Simplifying x2 + -70x + 25 = 0 Reorder the terms: 25 + -70x + x2 = 0 Solving 25 + -70x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -70x + -25 + x2 = 0 + -25 Reorder the terms: 25 + -25 + -70x + x2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -70x + x2 = 0 + -25 -70x + x2 = 0 + -25 Combine like terms: 0 + -25 = -25 -70x + x2 = -25 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 = -25 + 1225 Reorder the terms: 1225 + -70x + x2 = -25 + 1225 Combine like terms: -25 + 1225 = 1200 1225 + -70x + x2 = 1200 Factor a perfect square on the left side: (x + -35)(x + -35) = 1200 Calculate the square root of the right side: 34.641016151 Break this problem into two subproblems by setting (x + -35) equal to 34.641016151 and -34.641016151.Subproblem 1
x + -35 = 34.641016151 Simplifying x + -35 = 34.641016151 Reorder the terms: -35 + x = 34.641016151 Solving -35 + x = 34.641016151 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 = 34.641016151 + 35 Combine like terms: -35 + 35 = 0 0 + x = 34.641016151 + 35 x = 34.641016151 + 35 Combine like terms: 34.641016151 + 35 = 69.641016151 x = 69.641016151 Simplifying x = 69.641016151Subproblem 2
x + -35 = -34.641016151 Simplifying x + -35 = -34.641016151 Reorder the terms: -35 + x = -34.641016151 Solving -35 + x = -34.641016151 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 = -34.641016151 + 35 Combine like terms: -35 + 35 = 0 0 + x = -34.641016151 + 35 x = -34.641016151 + 35 Combine like terms: -34.641016151 + 35 = 0.358983849 x = 0.358983849 Simplifying x = 0.358983849Solution
The solution to the problem is based on the solutions from the subproblems. x = {69.641016151, 0.358983849}
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