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Simplifying -1x2 + 80x + -300 = 1220 Reorder the terms: -300 + 80x + -1x2 = 1220 Solving -300 + 80x + -1x2 = 1220 Solving for variable 'x'. Reorder the terms: -300 + -1220 + 80x + -1x2 = 1220 + -1220 Combine like terms: -300 + -1220 = -1520 -1520 + 80x + -1x2 = 1220 + -1220 Combine like terms: 1220 + -1220 = 0 -1520 + 80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1520 + -80x + x2 = 0 Move the constant term to the right: Add '-1520' to each side of the equation. 1520 + -80x + -1520 + x2 = 0 + -1520 Reorder the terms: 1520 + -1520 + -80x + x2 = 0 + -1520 Combine like terms: 1520 + -1520 = 0 0 + -80x + x2 = 0 + -1520 -80x + x2 = 0 + -1520 Combine like terms: 0 + -1520 = -1520 -80x + x2 = -1520 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 = -1520 + 1600 Reorder the terms: 1600 + -80x + x2 = -1520 + 1600 Combine like terms: -1520 + 1600 = 80 1600 + -80x + x2 = 80 Factor a perfect square on the left side: (x + -40)(x + -40) = 80 Calculate the square root of the right side: 8.94427191 Break this problem into two subproblems by setting (x + -40) equal to 8.94427191 and -8.94427191.Subproblem 1
x + -40 = 8.94427191 Simplifying x + -40 = 8.94427191 Reorder the terms: -40 + x = 8.94427191 Solving -40 + x = 8.94427191 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 = 8.94427191 + 40 Combine like terms: -40 + 40 = 0 0 + x = 8.94427191 + 40 x = 8.94427191 + 40 Combine like terms: 8.94427191 + 40 = 48.94427191 x = 48.94427191 Simplifying x = 48.94427191Subproblem 2
x + -40 = -8.94427191 Simplifying x + -40 = -8.94427191 Reorder the terms: -40 + x = -8.94427191 Solving -40 + x = -8.94427191 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 = -8.94427191 + 40 Combine like terms: -40 + 40 = 0 0 + x = -8.94427191 + 40 x = -8.94427191 + 40 Combine like terms: -8.94427191 + 40 = 31.05572809 x = 31.05572809 Simplifying x = 31.05572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {48.94427191, 31.05572809}
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