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Simplifying x2 + 17x + -225 = 0 Reorder the terms: -225 + 17x + x2 = 0 Solving -225 + 17x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 17x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 17x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 17x + x2 = 0 + 225 17x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 17x + x2 = 225 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = 225 + 72.25 Reorder the terms: 72.25 + 17x + x2 = 225 + 72.25 Combine like terms: 225 + 72.25 = 297.25 72.25 + 17x + x2 = 297.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 297.25 Calculate the square root of the right side: 17.24093965 Break this problem into two subproblems by setting (x + 8.5) equal to 17.24093965 and -17.24093965.Subproblem 1
x + 8.5 = 17.24093965 Simplifying x + 8.5 = 17.24093965 Reorder the terms: 8.5 + x = 17.24093965 Solving 8.5 + x = 17.24093965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 17.24093965 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 17.24093965 + -8.5 x = 17.24093965 + -8.5 Combine like terms: 17.24093965 + -8.5 = 8.74093965 x = 8.74093965 Simplifying x = 8.74093965Subproblem 2
x + 8.5 = -17.24093965 Simplifying x + 8.5 = -17.24093965 Reorder the terms: 8.5 + x = -17.24093965 Solving 8.5 + x = -17.24093965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -17.24093965 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -17.24093965 + -8.5 x = -17.24093965 + -8.5 Combine like terms: -17.24093965 + -8.5 = -25.74093965 x = -25.74093965 Simplifying x = -25.74093965Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.74093965, -25.74093965}
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