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Simplifying 500 = 80x + -1x2 Solving 500 = 80x + -1x2 Solving for variable 'x'. Reorder the terms: 500 + -80x + x2 = 80x + -80x + -1x2 + x2 Combine like terms: 80x + -80x = 0 500 + -80x + x2 = 0 + -1x2 + x2 500 + -80x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 500 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-500' to each side of the equation. 500 + -80x + -500 + x2 = 0 + -500 Reorder the terms: 500 + -500 + -80x + x2 = 0 + -500 Combine like terms: 500 + -500 = 0 0 + -80x + x2 = 0 + -500 -80x + x2 = 0 + -500 Combine like terms: 0 + -500 = -500 -80x + x2 = -500 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 = -500 + 1600 Reorder the terms: 1600 + -80x + x2 = -500 + 1600 Combine like terms: -500 + 1600 = 1100 1600 + -80x + x2 = 1100 Factor a perfect square on the left side: (x + -40)(x + -40) = 1100 Calculate the square root of the right side: 33.166247904 Break this problem into two subproblems by setting (x + -40) equal to 33.166247904 and -33.166247904.Subproblem 1
x + -40 = 33.166247904 Simplifying x + -40 = 33.166247904 Reorder the terms: -40 + x = 33.166247904 Solving -40 + x = 33.166247904 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 = 33.166247904 + 40 Combine like terms: -40 + 40 = 0 0 + x = 33.166247904 + 40 x = 33.166247904 + 40 Combine like terms: 33.166247904 + 40 = 73.166247904 x = 73.166247904 Simplifying x = 73.166247904Subproblem 2
x + -40 = -33.166247904 Simplifying x + -40 = -33.166247904 Reorder the terms: -40 + x = -33.166247904 Solving -40 + x = -33.166247904 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 = -33.166247904 + 40 Combine like terms: -40 + 40 = 0 0 + x = -33.166247904 + 40 x = -33.166247904 + 40 Combine like terms: -33.166247904 + 40 = 6.833752096 x = 6.833752096 Simplifying x = 6.833752096Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.166247904, 6.833752096}
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