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Simplifying x2 + -360x + -34.8 = 0 Reorder the terms: -34.8 + -360x + x2 = 0 Solving -34.8 + -360x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34.8' to each side of the equation. -34.8 + -360x + 34.8 + x2 = 0 + 34.8 Reorder the terms: -34.8 + 34.8 + -360x + x2 = 0 + 34.8 Combine like terms: -34.8 + 34.8 = 0.0 0.0 + -360x + x2 = 0 + 34.8 -360x + x2 = 0 + 34.8 Combine like terms: 0 + 34.8 = 34.8 -360x + x2 = 34.8 The x term is -360x. Take half its coefficient (-180). Square it (32400) and add it to both sides. Add '32400' to each side of the equation. -360x + 32400 + x2 = 34.8 + 32400 Reorder the terms: 32400 + -360x + x2 = 34.8 + 32400 Combine like terms: 34.8 + 32400 = 32434.8 32400 + -360x + x2 = 32434.8 Factor a perfect square on the left side: (x + -180)(x + -180) = 32434.8 Calculate the square root of the right side: 180.096640724 Break this problem into two subproblems by setting (x + -180) equal to 180.096640724 and -180.096640724.Subproblem 1
x + -180 = 180.096640724 Simplifying x + -180 = 180.096640724 Reorder the terms: -180 + x = 180.096640724 Solving -180 + x = 180.096640724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = 180.096640724 + 180 Combine like terms: -180 + 180 = 0 0 + x = 180.096640724 + 180 x = 180.096640724 + 180 Combine like terms: 180.096640724 + 180 = 360.096640724 x = 360.096640724 Simplifying x = 360.096640724Subproblem 2
x + -180 = -180.096640724 Simplifying x + -180 = -180.096640724 Reorder the terms: -180 + x = -180.096640724 Solving -180 + x = -180.096640724 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = -180.096640724 + 180 Combine like terms: -180 + 180 = 0 0 + x = -180.096640724 + 180 x = -180.096640724 + 180 Combine like terms: -180.096640724 + 180 = -0.096640724 x = -0.096640724 Simplifying x = -0.096640724Solution
The solution to the problem is based on the solutions from the subproblems. x = {360.096640724, -0.096640724}
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