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Simplifying x2 + 35x + -234 = 0 Reorder the terms: -234 + 35x + x2 = 0 Solving -234 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '234' to each side of the equation. -234 + 35x + 234 + x2 = 0 + 234 Reorder the terms: -234 + 234 + 35x + x2 = 0 + 234 Combine like terms: -234 + 234 = 0 0 + 35x + x2 = 0 + 234 35x + x2 = 0 + 234 Combine like terms: 0 + 234 = 234 35x + x2 = 234 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 = 234 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 234 + 306.25 Combine like terms: 234 + 306.25 = 540.25 306.25 + 35x + x2 = 540.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 540.25 Calculate the square root of the right side: 23.243278598 Break this problem into two subproblems by setting (x + 17.5) equal to 23.243278598 and -23.243278598.Subproblem 1
x + 17.5 = 23.243278598 Simplifying x + 17.5 = 23.243278598 Reorder the terms: 17.5 + x = 23.243278598 Solving 17.5 + x = 23.243278598 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 = 23.243278598 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 23.243278598 + -17.5 x = 23.243278598 + -17.5 Combine like terms: 23.243278598 + -17.5 = 5.743278598 x = 5.743278598 Simplifying x = 5.743278598Subproblem 2
x + 17.5 = -23.243278598 Simplifying x + 17.5 = -23.243278598 Reorder the terms: 17.5 + x = -23.243278598 Solving 17.5 + x = -23.243278598 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 = -23.243278598 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -23.243278598 + -17.5 x = -23.243278598 + -17.5 Combine like terms: -23.243278598 + -17.5 = -40.743278598 x = -40.743278598 Simplifying x = -40.743278598Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.743278598, -40.743278598}
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