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Simplifying 0 = x2 + 80x + -700 Reorder the terms: 0 = -700 + 80x + x2 Solving 0 = -700 + 80x + x2 Solving for variable 'x'. Combine like terms: 0 + 700 = 700 700 + -80x + -1x2 = -700 + 80x + x2 + 700 + -80x + -1x2 Reorder the terms: 700 + -80x + -1x2 = -700 + 700 + 80x + -80x + x2 + -1x2 Combine like terms: -700 + 700 = 0 700 + -80x + -1x2 = 0 + 80x + -80x + x2 + -1x2 700 + -80x + -1x2 = 80x + -80x + x2 + -1x2 Combine like terms: 80x + -80x = 0 700 + -80x + -1x2 = 0 + x2 + -1x2 700 + -80x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 700 + -80x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -700 + 80x + x2 = 0 Move the constant term to the right: Add '700' to each side of the equation. -700 + 80x + 700 + x2 = 0 + 700 Reorder the terms: -700 + 700 + 80x + x2 = 0 + 700 Combine like terms: -700 + 700 = 0 0 + 80x + x2 = 0 + 700 80x + x2 = 0 + 700 Combine like terms: 0 + 700 = 700 80x + x2 = 700 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 = 700 + 1600 Reorder the terms: 1600 + 80x + x2 = 700 + 1600 Combine like terms: 700 + 1600 = 2300 1600 + 80x + x2 = 2300 Factor a perfect square on the left side: (x + 40)(x + 40) = 2300 Calculate the square root of the right side: 47.958315233 Break this problem into two subproblems by setting (x + 40) equal to 47.958315233 and -47.958315233.Subproblem 1
x + 40 = 47.958315233 Simplifying x + 40 = 47.958315233 Reorder the terms: 40 + x = 47.958315233 Solving 40 + x = 47.958315233 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 = 47.958315233 + -40 Combine like terms: 40 + -40 = 0 0 + x = 47.958315233 + -40 x = 47.958315233 + -40 Combine like terms: 47.958315233 + -40 = 7.958315233 x = 7.958315233 Simplifying x = 7.958315233Subproblem 2
x + 40 = -47.958315233 Simplifying x + 40 = -47.958315233 Reorder the terms: 40 + x = -47.958315233 Solving 40 + x = -47.958315233 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 = -47.958315233 + -40 Combine like terms: 40 + -40 = 0 0 + x = -47.958315233 + -40 x = -47.958315233 + -40 Combine like terms: -47.958315233 + -40 = -87.958315233 x = -87.958315233 Simplifying x = -87.958315233Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.958315233, -87.958315233}
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