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Simplifying -1x2 + 80x + -300 = 0 Reorder the terms: -300 + 80x + -1x2 = 0 Solving -300 + 80x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 300 + -80x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -80x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -80x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -80x + x2 = 0 + -300 -80x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -80x + x2 = -300 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 = -300 + 1600 Reorder the terms: 1600 + -80x + x2 = -300 + 1600 Combine like terms: -300 + 1600 = 1300 1600 + -80x + x2 = 1300 Factor a perfect square on the left side: (x + -40)(x + -40) = 1300 Calculate the square root of the right side: 36.055512755 Break this problem into two subproblems by setting (x + -40) equal to 36.055512755 and -36.055512755.Subproblem 1
x + -40 = 36.055512755 Simplifying x + -40 = 36.055512755 Reorder the terms: -40 + x = 36.055512755 Solving -40 + x = 36.055512755 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 = 36.055512755 + 40 Combine like terms: -40 + 40 = 0 0 + x = 36.055512755 + 40 x = 36.055512755 + 40 Combine like terms: 36.055512755 + 40 = 76.055512755 x = 76.055512755 Simplifying x = 76.055512755Subproblem 2
x + -40 = -36.055512755 Simplifying x + -40 = -36.055512755 Reorder the terms: -40 + x = -36.055512755 Solving -40 + x = -36.055512755 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 = -36.055512755 + 40 Combine like terms: -40 + 40 = 0 0 + x = -36.055512755 + 40 x = -36.055512755 + 40 Combine like terms: -36.055512755 + 40 = 3.944487245 x = 3.944487245 Simplifying x = 3.944487245Solution
The solution to the problem is based on the solutions from the subproblems. x = {76.055512755, 3.944487245}
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