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Simplifying x2 + 0.5x + -170 = 0 Reorder the terms: -170 + 0.5x + x2 = 0 Solving -170 + 0.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 0.5x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 0.5x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 0.5x + x2 = 0 + 170 0.5x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 0.5x + x2 = 170 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 170 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 170 + 0.0625 Combine like terms: 170 + 0.0625 = 170.0625 0.0625 + 0.5x + x2 = 170.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 170.0625 Calculate the square root of the right side: 13.040801356 Break this problem into two subproblems by setting (x + 0.25) equal to 13.040801356 and -13.040801356.Subproblem 1
x + 0.25 = 13.040801356 Simplifying x + 0.25 = 13.040801356 Reorder the terms: 0.25 + x = 13.040801356 Solving 0.25 + x = 13.040801356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 13.040801356 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 13.040801356 + -0.25 x = 13.040801356 + -0.25 Combine like terms: 13.040801356 + -0.25 = 12.790801356 x = 12.790801356 Simplifying x = 12.790801356Subproblem 2
x + 0.25 = -13.040801356 Simplifying x + 0.25 = -13.040801356 Reorder the terms: 0.25 + x = -13.040801356 Solving 0.25 + x = -13.040801356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -13.040801356 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -13.040801356 + -0.25 x = -13.040801356 + -0.25 Combine like terms: -13.040801356 + -0.25 = -13.290801356 x = -13.290801356 Simplifying x = -13.290801356Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.790801356, -13.290801356}
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