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Simplifying -7x(10 + -1x) = 58 (10 * -7x + -1x * -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 = 33.285714286 25 + -10x + x2 = 33.285714286 Factor a perfect square on the left side: (x + -5)(x + -5) = 33.285714286 Calculate the square root of the right side: 5.769377288 Break this problem into two subproblems by setting (x + -5) equal to 5.769377288 and -5.769377288.Subproblem 1
x + -5 = 5.769377288 Simplifying x + -5 = 5.769377288 Reorder the terms: -5 + x = 5.769377288 Solving -5 + x = 5.769377288 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 = 5.769377288 + 5 Combine like terms: -5 + 5 = 0 0 + x = 5.769377288 + 5 x = 5.769377288 + 5 Combine like terms: 5.769377288 + 5 = 10.769377288 x = 10.769377288 Simplifying x = 10.769377288Subproblem 2
x + -5 = -5.769377288 Simplifying x + -5 = -5.769377288 Reorder the terms: -5 + x = -5.769377288 Solving -5 + x = -5.769377288 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 = -5.769377288 + 5 Combine like terms: -5 + 5 = 0 0 + x = -5.769377288 + 5 x = -5.769377288 + 5 Combine like terms: -5.769377288 + 5 = -0.769377288 x = -0.769377288 Simplifying x = -0.769377288Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.769377288, -0.769377288}
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