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Simplifying 7x2 + 18x + -35 = 0 Reorder the terms: -35 + 18x + 7x2 = 0 Solving -35 + 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'. -5 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 2.571428571x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2.571428571x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2.571428571x + x2 = 0 + 5 2.571428571x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2.571428571x + x2 = 5 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 = 5 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = 5 + 1.653061225 Combine like terms: 5 + 1.653061225 = 6.653061225 1.653061225 + 2.571428571x + x2 = 6.653061225 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 6.653061225 Calculate the square root of the right side: 2.579352869 Break this problem into two subproblems by setting (x + 1.285714286) equal to 2.579352869 and -2.579352869.Subproblem 1
x + 1.285714286 = 2.579352869 Simplifying x + 1.285714286 = 2.579352869 Reorder the terms: 1.285714286 + x = 2.579352869 Solving 1.285714286 + x = 2.579352869 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 = 2.579352869 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 2.579352869 + -1.285714286 x = 2.579352869 + -1.285714286 Combine like terms: 2.579352869 + -1.285714286 = 1.293638583 x = 1.293638583 Simplifying x = 1.293638583Subproblem 2
x + 1.285714286 = -2.579352869 Simplifying x + 1.285714286 = -2.579352869 Reorder the terms: 1.285714286 + x = -2.579352869 Solving 1.285714286 + x = -2.579352869 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 = -2.579352869 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -2.579352869 + -1.285714286 x = -2.579352869 + -1.285714286 Combine like terms: -2.579352869 + -1.285714286 = -3.865067155 x = -3.865067155 Simplifying x = -3.865067155Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.293638583, -3.865067155}
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