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Simplifying 0 = x2 + -80x + 900 Reorder the terms: 0 = 900 + -80x + x2 Solving 0 = 900 + -80x + x2 Solving for variable 'x'. Combine like terms: 0 + -900 = -900 -900 + 80x + -1x2 = 900 + -80x + x2 + -900 + 80x + -1x2 Reorder the terms: -900 + 80x + -1x2 = 900 + -900 + -80x + 80x + x2 + -1x2 Combine like terms: 900 + -900 = 0 -900 + 80x + -1x2 = 0 + -80x + 80x + x2 + -1x2 -900 + 80x + -1x2 = -80x + 80x + x2 + -1x2 Combine like terms: -80x + 80x = 0 -900 + 80x + -1x2 = 0 + x2 + -1x2 -900 + 80x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -900 + 80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 900 + -80x + x2 = 0 Move the constant term to the right: Add '-900' to each side of the equation. 900 + -80x + -900 + x2 = 0 + -900 Reorder the terms: 900 + -900 + -80x + x2 = 0 + -900 Combine like terms: 900 + -900 = 0 0 + -80x + x2 = 0 + -900 -80x + x2 = 0 + -900 Combine like terms: 0 + -900 = -900 -80x + x2 = -900 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 = -900 + 1600 Reorder the terms: 1600 + -80x + x2 = -900 + 1600 Combine like terms: -900 + 1600 = 700 1600 + -80x + x2 = 700 Factor a perfect square on the left side: (x + -40)(x + -40) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (x + -40) equal to 26.457513111 and -26.457513111.Subproblem 1
x + -40 = 26.457513111 Simplifying x + -40 = 26.457513111 Reorder the terms: -40 + x = 26.457513111 Solving -40 + x = 26.457513111 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 = 26.457513111 + 40 Combine like terms: -40 + 40 = 0 0 + x = 26.457513111 + 40 x = 26.457513111 + 40 Combine like terms: 26.457513111 + 40 = 66.457513111 x = 66.457513111 Simplifying x = 66.457513111Subproblem 2
x + -40 = -26.457513111 Simplifying x + -40 = -26.457513111 Reorder the terms: -40 + x = -26.457513111 Solving -40 + x = -26.457513111 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 = -26.457513111 + 40 Combine like terms: -40 + 40 = 0 0 + x = -26.457513111 + 40 x = -26.457513111 + 40 Combine like terms: -26.457513111 + 40 = 13.542486889 x = 13.542486889 Simplifying x = 13.542486889Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.457513111, 13.542486889}
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