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Simplifying x2 + 35x + -342 = 0 Reorder the terms: -342 + 35x + x2 = 0 Solving -342 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '342' to each side of the equation. -342 + 35x + 342 + x2 = 0 + 342 Reorder the terms: -342 + 342 + 35x + x2 = 0 + 342 Combine like terms: -342 + 342 = 0 0 + 35x + x2 = 0 + 342 35x + x2 = 0 + 342 Combine like terms: 0 + 342 = 342 35x + x2 = 342 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 = 342 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 342 + 306.25 Combine like terms: 342 + 306.25 = 648.25 306.25 + 35x + x2 = 648.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 648.25 Calculate the square root of the right side: 25.460754113 Break this problem into two subproblems by setting (x + 17.5) equal to 25.460754113 and -25.460754113.Subproblem 1
x + 17.5 = 25.460754113 Simplifying x + 17.5 = 25.460754113 Reorder the terms: 17.5 + x = 25.460754113 Solving 17.5 + x = 25.460754113 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 = 25.460754113 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 25.460754113 + -17.5 x = 25.460754113 + -17.5 Combine like terms: 25.460754113 + -17.5 = 7.960754113 x = 7.960754113 Simplifying x = 7.960754113Subproblem 2
x + 17.5 = -25.460754113 Simplifying x + 17.5 = -25.460754113 Reorder the terms: 17.5 + x = -25.460754113 Solving 17.5 + x = -25.460754113 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 = -25.460754113 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -25.460754113 + -17.5 x = -25.460754113 + -17.5 Combine like terms: -25.460754113 + -17.5 = -42.960754113 x = -42.960754113 Simplifying x = -42.960754113Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.960754113, -42.960754113}
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