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Simplifying x2 + 35x + -64 = 0 Reorder the terms: -64 + 35x + x2 = 0 Solving -64 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + 35x + 64 + x2 = 0 + 64 Reorder the terms: -64 + 64 + 35x + x2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + 35x + x2 = 0 + 64 35x + x2 = 0 + 64 Combine like terms: 0 + 64 = 64 35x + x2 = 64 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 = 64 + 306.25 Reorder the terms: 306.25 + 35x + x2 = 64 + 306.25 Combine like terms: 64 + 306.25 = 370.25 306.25 + 35x + x2 = 370.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 370.25 Calculate the square root of the right side: 19.241881405 Break this problem into two subproblems by setting (x + 17.5) equal to 19.241881405 and -19.241881405.Subproblem 1
x + 17.5 = 19.241881405 Simplifying x + 17.5 = 19.241881405 Reorder the terms: 17.5 + x = 19.241881405 Solving 17.5 + x = 19.241881405 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 = 19.241881405 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 19.241881405 + -17.5 x = 19.241881405 + -17.5 Combine like terms: 19.241881405 + -17.5 = 1.741881405 x = 1.741881405 Simplifying x = 1.741881405Subproblem 2
x + 17.5 = -19.241881405 Simplifying x + 17.5 = -19.241881405 Reorder the terms: 17.5 + x = -19.241881405 Solving 17.5 + x = -19.241881405 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 = -19.241881405 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -19.241881405 + -17.5 x = -19.241881405 + -17.5 Combine like terms: -19.241881405 + -17.5 = -36.741881405 x = -36.741881405 Simplifying x = -36.741881405Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.741881405, -36.741881405}
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