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Simplifying 7x2 + 46x + -80 = 2 Reorder the terms: -80 + 46x + 7x2 = 2 Solving -80 + 46x + 7x2 = 2 Solving for variable 'x'. Reorder the terms: -80 + -2 + 46x + 7x2 = 2 + -2 Combine like terms: -80 + -2 = -82 -82 + 46x + 7x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -82 + 46x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -11.71428571 + 6.571428571x + x2 = 0 Move the constant term to the right: Add '11.71428571' to each side of the equation. -11.71428571 + 6.571428571x + 11.71428571 + x2 = 0 + 11.71428571 Reorder the terms: -11.71428571 + 11.71428571 + 6.571428571x + x2 = 0 + 11.71428571 Combine like terms: -11.71428571 + 11.71428571 = 0.00000000 0.00000000 + 6.571428571x + x2 = 0 + 11.71428571 6.571428571x + x2 = 0 + 11.71428571 Combine like terms: 0 + 11.71428571 = 11.71428571 6.571428571x + x2 = 11.71428571 The x term is 6.571428571x. Take half its coefficient (3.285714286). Square it (10.79591837) and add it to both sides. Add '10.79591837' to each side of the equation. 6.571428571x + 10.79591837 + x2 = 11.71428571 + 10.79591837 Reorder the terms: 10.79591837 + 6.571428571x + x2 = 11.71428571 + 10.79591837 Combine like terms: 11.71428571 + 10.79591837 = 22.51020408 10.79591837 + 6.571428571x + x2 = 22.51020408 Factor a perfect square on the left side: (x + 3.285714286)(x + 3.285714286) = 22.51020408 Calculate the square root of the right side: 4.744491973 Break this problem into two subproblems by setting (x + 3.285714286) equal to 4.744491973 and -4.744491973.Subproblem 1
x + 3.285714286 = 4.744491973 Simplifying x + 3.285714286 = 4.744491973 Reorder the terms: 3.285714286 + x = 4.744491973 Solving 3.285714286 + x = 4.744491973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = 4.744491973 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = 4.744491973 + -3.285714286 x = 4.744491973 + -3.285714286 Combine like terms: 4.744491973 + -3.285714286 = 1.458777687 x = 1.458777687 Simplifying x = 1.458777687Subproblem 2
x + 3.285714286 = -4.744491973 Simplifying x + 3.285714286 = -4.744491973 Reorder the terms: 3.285714286 + x = -4.744491973 Solving 3.285714286 + x = -4.744491973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = -4.744491973 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = -4.744491973 + -3.285714286 x = -4.744491973 + -3.285714286 Combine like terms: -4.744491973 + -3.285714286 = -8.030206259 x = -8.030206259 Simplifying x = -8.030206259Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.458777687, -8.030206259}
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