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Simplifying 5x2 + 56x + -960 = 0 Reorder the terms: -960 + 56x + 5x2 = 0 Solving -960 + 56x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -192 + 11.2x + x2 = 0 Move the constant term to the right: Add '192' to each side of the equation. -192 + 11.2x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + 11.2x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 11.2x + x2 = 0 + 192 11.2x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 11.2x + x2 = 192 The x term is 11.2x. Take half its coefficient (5.6). Square it (31.36) and add it to both sides. Add '31.36' to each side of the equation. 11.2x + 31.36 + x2 = 192 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 192 + 31.36 Combine like terms: 192 + 31.36 = 223.36 31.36 + 11.2x + x2 = 223.36 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 223.36 Calculate the square root of the right side: 14.945233354 Break this problem into two subproblems by setting (x + 5.6) equal to 14.945233354 and -14.945233354.Subproblem 1
x + 5.6 = 14.945233354 Simplifying x + 5.6 = 14.945233354 Reorder the terms: 5.6 + x = 14.945233354 Solving 5.6 + x = 14.945233354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = 14.945233354 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 14.945233354 + -5.6 x = 14.945233354 + -5.6 Combine like terms: 14.945233354 + -5.6 = 9.345233354 x = 9.345233354 Simplifying x = 9.345233354Subproblem 2
x + 5.6 = -14.945233354 Simplifying x + 5.6 = -14.945233354 Reorder the terms: 5.6 + x = -14.945233354 Solving 5.6 + x = -14.945233354 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.6' to each side of the equation. 5.6 + -5.6 + x = -14.945233354 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -14.945233354 + -5.6 x = -14.945233354 + -5.6 Combine like terms: -14.945233354 + -5.6 = -20.545233354 x = -20.545233354 Simplifying x = -20.545233354Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.345233354, -20.545233354}
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