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Simplifying x2 + 35x + 18 = 0 Reorder the terms: 18 + 35x + x2 = 0 Solving 18 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + 35x + -18 + x2 = 0 + -18 Reorder the terms: 18 + -18 + 35x + x2 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 35x + x2 = 0 + -18 35x + x2 = 0 + -18 Combine like terms: 0 + -18 = -18 35x + x2 = -18 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 = -18 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -18 + 306.25 Combine like terms: -18 + 306.25 = 288.25 306.25 + 35x + x2 = 288.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 288.25 Calculate the square root of the right side: 16.977926846 Break this problem into two subproblems by setting (x + 17.5) equal to 16.977926846 and -16.977926846.Subproblem 1
x + 17.5 = 16.977926846 Simplifying x + 17.5 = 16.977926846 Reorder the terms: 17.5 + x = 16.977926846 Solving 17.5 + x = 16.977926846 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 = 16.977926846 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 16.977926846 + -17.5 x = 16.977926846 + -17.5 Combine like terms: 16.977926846 + -17.5 = -0.522073154 x = -0.522073154 Simplifying x = -0.522073154Subproblem 2
x + 17.5 = -16.977926846 Simplifying x + 17.5 = -16.977926846 Reorder the terms: 17.5 + x = -16.977926846 Solving 17.5 + x = -16.977926846 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 = -16.977926846 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -16.977926846 + -17.5 x = -16.977926846 + -17.5 Combine like terms: -16.977926846 + -17.5 = -34.477926846 x = -34.477926846 Simplifying x = -34.477926846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.522073154, -34.477926846}
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