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Simplifying 7x2 + 8x = -10x + -1 Reorder the terms: 8x + 7x2 = -10x + -1 Reorder the terms: 8x + 7x2 = -1 + -10x Solving 8x + 7x2 = -1 + -10x Solving for variable 'x'. Reorder the terms: 1 + 8x + 10x + 7x2 = -1 + -10x + 1 + 10x Combine like terms: 8x + 10x = 18x 1 + 18x + 7x2 = -1 + -10x + 1 + 10x Reorder the terms: 1 + 18x + 7x2 = -1 + 1 + -10x + 10x Combine like terms: -1 + 1 = 0 1 + 18x + 7x2 = 0 + -10x + 10x 1 + 18x + 7x2 = -10x + 10x Combine like terms: -10x + 10x = 0 1 + 18x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + 2.571428571x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 2.571428571x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 2.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 2.571428571x + x2 = 0 + -0.1428571429 2.571428571x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 2.571428571x + x2 = -0.1428571429 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 = -0.1428571429 + 1.653061225 Reorder the terms: 1.653061225 + 2.571428571x + x2 = -0.1428571429 + 1.653061225 Combine like terms: -0.1428571429 + 1.653061225 = 1.5102040821 1.653061225 + 2.571428571x + x2 = 1.5102040821 Factor a perfect square on the left side: (x + 1.285714286)(x + 1.285714286) = 1.5102040821 Calculate the square root of the right side: 1.22890361 Break this problem into two subproblems by setting (x + 1.285714286) equal to 1.22890361 and -1.22890361.Subproblem 1
x + 1.285714286 = 1.22890361 Simplifying x + 1.285714286 = 1.22890361 Reorder the terms: 1.285714286 + x = 1.22890361 Solving 1.285714286 + x = 1.22890361 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 = 1.22890361 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = 1.22890361 + -1.285714286 x = 1.22890361 + -1.285714286 Combine like terms: 1.22890361 + -1.285714286 = -0.056810676 x = -0.056810676 Simplifying x = -0.056810676Subproblem 2
x + 1.285714286 = -1.22890361 Simplifying x + 1.285714286 = -1.22890361 Reorder the terms: 1.285714286 + x = -1.22890361 Solving 1.285714286 + x = -1.22890361 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 = -1.22890361 + -1.285714286 Combine like terms: 1.285714286 + -1.285714286 = 0.000000000 0.000000000 + x = -1.22890361 + -1.285714286 x = -1.22890361 + -1.285714286 Combine like terms: -1.22890361 + -1.285714286 = -2.514617896 x = -2.514617896 Simplifying x = -2.514617896Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.056810676, -2.514617896}
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