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Simplifying 0.5x2 + -40x + 408 = 0 Reorder the terms: 408 + -40x + 0.5x2 = 0 Solving 408 + -40x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 816 + -80x + x2 = 0 Move the constant term to the right: Add '-816' to each side of the equation. 816 + -80x + -816 + x2 = 0 + -816 Reorder the terms: 816 + -816 + -80x + x2 = 0 + -816 Combine like terms: 816 + -816 = 0 0 + -80x + x2 = 0 + -816 -80x + x2 = 0 + -816 Combine like terms: 0 + -816 = -816 -80x + x2 = -816 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -816 + 1600 Reorder the terms: 1600 + -80x + x2 = -816 + 1600 Combine like terms: -816 + 1600 = 784 1600 + -80x + x2 = 784 Factor a perfect square on the left side: (x + -40)(x + -40) = 784 Calculate the square root of the right side: 28 Break this problem into two subproblems by setting (x + -40) equal to 28 and -28.Subproblem 1
x + -40 = 28 Simplifying x + -40 = 28 Reorder the terms: -40 + x = 28 Solving -40 + x = 28 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 28 + 40 Combine like terms: -40 + 40 = 0 0 + x = 28 + 40 x = 28 + 40 Combine like terms: 28 + 40 = 68 x = 68 Simplifying x = 68Subproblem 2
x + -40 = -28 Simplifying x + -40 = -28 Reorder the terms: -40 + x = -28 Solving -40 + x = -28 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -28 + 40 Combine like terms: -40 + 40 = 0 0 + x = -28 + 40 x = -28 + 40 Combine like terms: -28 + 40 = 12 x = 12 Simplifying x = 12Solution
The solution to the problem is based on the solutions from the subproblems. x = {68, 12}
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