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Simplifying x2 + -80x = 1500 Reorder the terms: -80x + x2 = 1500 Solving -80x + x2 = 1500 Solving for variable 'x'. Reorder the terms: -1500 + -80x + x2 = 1500 + -1500 Combine like terms: 1500 + -1500 = 0 -1500 + -80x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1500' to each side of the equation. -1500 + -80x + 1500 + x2 = 0 + 1500 Reorder the terms: -1500 + 1500 + -80x + x2 = 0 + 1500 Combine like terms: -1500 + 1500 = 0 0 + -80x + x2 = 0 + 1500 -80x + x2 = 0 + 1500 Combine like terms: 0 + 1500 = 1500 -80x + x2 = 1500 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 = 1500 + 1600 Reorder the terms: 1600 + -80x + x2 = 1500 + 1600 Combine like terms: 1500 + 1600 = 3100 1600 + -80x + x2 = 3100 Factor a perfect square on the left side: (x + -40)(x + -40) = 3100 Calculate the square root of the right side: 55.677643628 Break this problem into two subproblems by setting (x + -40) equal to 55.677643628 and -55.677643628.Subproblem 1
x + -40 = 55.677643628 Simplifying x + -40 = 55.677643628 Reorder the terms: -40 + x = 55.677643628 Solving -40 + x = 55.677643628 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 = 55.677643628 + 40 Combine like terms: -40 + 40 = 0 0 + x = 55.677643628 + 40 x = 55.677643628 + 40 Combine like terms: 55.677643628 + 40 = 95.677643628 x = 95.677643628 Simplifying x = 95.677643628Subproblem 2
x + -40 = -55.677643628 Simplifying x + -40 = -55.677643628 Reorder the terms: -40 + x = -55.677643628 Solving -40 + x = -55.677643628 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 = -55.677643628 + 40 Combine like terms: -40 + 40 = 0 0 + x = -55.677643628 + 40 x = -55.677643628 + 40 Combine like terms: -55.677643628 + 40 = -15.677643628 x = -15.677643628 Simplifying x = -15.677643628Solution
The solution to the problem is based on the solutions from the subproblems. x = {95.677643628, -15.677643628}
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