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Simplifying x2 + -35x + 9 = 0 Reorder the terms: 9 + -35x + x2 = 0 Solving 9 + -35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -35x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -35x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -35x + x2 = 0 + -9 -35x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -35x + x2 = -9 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 = -9 + 306.25 Reorder the terms: 306.25 + -35x + x2 = -9 + 306.25 Combine like terms: -9 + 306.25 = 297.25 306.25 + -35x + x2 = 297.25 Factor a perfect square on the left side: (x + -17.5)(x + -17.5) = 297.25 Calculate the square root of the right side: 17.24093965 Break this problem into two subproblems by setting (x + -17.5) equal to 17.24093965 and -17.24093965.Subproblem 1
x + -17.5 = 17.24093965 Simplifying x + -17.5 = 17.24093965 Reorder the terms: -17.5 + x = 17.24093965 Solving -17.5 + x = 17.24093965 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 = 17.24093965 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 17.24093965 + 17.5 x = 17.24093965 + 17.5 Combine like terms: 17.24093965 + 17.5 = 34.74093965 x = 34.74093965 Simplifying x = 34.74093965Subproblem 2
x + -17.5 = -17.24093965 Simplifying x + -17.5 = -17.24093965 Reorder the terms: -17.5 + x = -17.24093965 Solving -17.5 + x = -17.24093965 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 = -17.24093965 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -17.24093965 + 17.5 x = -17.24093965 + 17.5 Combine like terms: -17.24093965 + 17.5 = 0.25906035 x = 0.25906035 Simplifying x = 0.25906035Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.74093965, 0.25906035}
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