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Simplifying 7x(10 + x) = -58 (10 * 7x + x * 7x) = -58 (70x + 7x2) = -58 Solving 70x + 7x2 = -58 Solving for variable 'x'. Reorder the terms: 58 + 70x + 7x2 = -58 + 58 Combine like terms: -58 + 58 = 0 58 + 70x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 8.285714286 + 10x + x2 = 0 Move the constant term to the right: Add '-8.285714286' to each side of the equation. 8.285714286 + 10x + -8.285714286 + x2 = 0 + -8.285714286 Reorder the terms: 8.285714286 + -8.285714286 + 10x + x2 = 0 + -8.285714286 Combine like terms: 8.285714286 + -8.285714286 = 0.000000000 0.000000000 + 10x + x2 = 0 + -8.285714286 10x + x2 = 0 + -8.285714286 Combine like terms: 0 + -8.285714286 = -8.285714286 10x + x2 = -8.285714286 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -8.285714286 + 25 Reorder the terms: 25 + 10x + x2 = -8.285714286 + 25 Combine like terms: -8.285714286 + 25 = 16.714285714 25 + 10x + x2 = 16.714285714 Factor a perfect square on the left side: (x + 5)(x + 5) = 16.714285714 Calculate the square root of the right side: 4.088310863 Break this problem into two subproblems by setting (x + 5) equal to 4.088310863 and -4.088310863.Subproblem 1
x + 5 = 4.088310863 Simplifying x + 5 = 4.088310863 Reorder the terms: 5 + x = 4.088310863 Solving 5 + x = 4.088310863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.088310863 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.088310863 + -5 x = 4.088310863 + -5 Combine like terms: 4.088310863 + -5 = -0.911689137 x = -0.911689137 Simplifying x = -0.911689137Subproblem 2
x + 5 = -4.088310863 Simplifying x + 5 = -4.088310863 Reorder the terms: 5 + x = -4.088310863 Solving 5 + x = -4.088310863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.088310863 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.088310863 + -5 x = -4.088310863 + -5 Combine like terms: -4.088310863 + -5 = -9.088310863 x = -9.088310863 Simplifying x = -9.088310863Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.911689137, -9.088310863}
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