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Simplifying x2 + -40x + 5.5 = 0 Reorder the terms: 5.5 + -40x + x2 = 0 Solving 5.5 + -40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + -40x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + -40x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + -40x + x2 = 0 + -5.5 -40x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 -40x + x2 = -5.5 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = -5.5 + 400 Reorder the terms: 400 + -40x + x2 = -5.5 + 400 Combine like terms: -5.5 + 400 = 394.5 400 + -40x + x2 = 394.5 Factor a perfect square on the left side: (x + -20)(x + -20) = 394.5 Calculate the square root of the right side: 19.862024066 Break this problem into two subproblems by setting (x + -20) equal to 19.862024066 and -19.862024066.Subproblem 1
x + -20 = 19.862024066 Simplifying x + -20 = 19.862024066 Reorder the terms: -20 + x = 19.862024066 Solving -20 + x = 19.862024066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.862024066 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.862024066 + 20 x = 19.862024066 + 20 Combine like terms: 19.862024066 + 20 = 39.862024066 x = 39.862024066 Simplifying x = 39.862024066Subproblem 2
x + -20 = -19.862024066 Simplifying x + -20 = -19.862024066 Reorder the terms: -20 + x = -19.862024066 Solving -20 + x = -19.862024066 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.862024066 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.862024066 + 20 x = -19.862024066 + 20 Combine like terms: -19.862024066 + 20 = 0.137975934 x = 0.137975934 Simplifying x = 0.137975934Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.862024066, 0.137975934}
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