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Simplifying 7x2 + 18x + -7 = 0 Reorder the terms: -7 + 18x + 7x2 = 0 Solving -7 + 18x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 2.571428571x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 2.571428571x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2.571428571x + x2 = 0 + 1 2.571428571x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 2.571428571x + x2 = 1 The x term is 2.571428571x. Take half its coefficient (1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. 2.571428571x + 1.653061225 + x2 = 1 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 1 + 1.653061225 Combine like terms: 1 + 1.653061225 = 2.653061225 1.653061225 + 2.571428571x + x2 = 2.653061225 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 2.653061225 Calculate the square root of the right side: 1.628822036 Break this problem into two subproblems by setting (x + 1.285714286) equal to 1.628822036 and -1.628822036.Subproblem 1
x + 1.285714286 = 1.628822036 Simplifying x + 1.285714286 = 1.628822036 Reorder the terms: 1.285714286 + x = 1.628822036 Solving 1.285714286 + x = 1.628822036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = 1.628822036 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 1.628822036 + -1.285714286 x = 1.628822036 + -1.285714286 Combine like terms: 1.628822036 + -1.285714286 = 0.34310775 x = 0.34310775 Simplifying x = 0.34310775Subproblem 2
x + 1.285714286 = -1.628822036 Simplifying x + 1.285714286 = -1.628822036 Reorder the terms: 1.285714286 + x = -1.628822036 Solving 1.285714286 + x = -1.628822036 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.285714286' to each side of the equation. 1.285714286 + -1.285714286 + x = -1.628822036 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -1.628822036 + -1.285714286 x = -1.628822036 + -1.285714286 Combine like terms: -1.628822036 + -1.285714286 = -2.914536322 x = -2.914536322 Simplifying x = -2.914536322Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34310775, -2.914536322}
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