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Simplifying 5x2 + 56x + -192 = 0 Reorder the terms: -192 + 56x + 5x2 = 0 Solving -192 + 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'. -38.4 + 11.2x + x2 = 0 Move the constant term to the right: Add '38.4' to each side of the equation. -38.4 + 11.2x + 38.4 + x2 = 0 + 38.4 Reorder the terms: -38.4 + 38.4 + 11.2x + x2 = 0 + 38.4 Combine like terms: -38.4 + 38.4 = 0.0 0.0 + 11.2x + x2 = 0 + 38.4 11.2x + x2 = 0 + 38.4 Combine like terms: 0 + 38.4 = 38.4 11.2x + x2 = 38.4 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 = 38.4 + 31.36 Reorder the terms: 31.36 + 11.2x + x2 = 38.4 + 31.36 Combine like terms: 38.4 + 31.36 = 69.76 31.36 + 11.2x + x2 = 69.76 Factor a perfect square on the left side: (x + 5.6)(x + 5.6) = 69.76 Calculate the square root of the right side: 8.352245207 Break this problem into two subproblems by setting (x + 5.6) equal to 8.352245207 and -8.352245207.Subproblem 1
x + 5.6 = 8.352245207 Simplifying x + 5.6 = 8.352245207 Reorder the terms: 5.6 + x = 8.352245207 Solving 5.6 + x = 8.352245207 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 = 8.352245207 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = 8.352245207 + -5.6 x = 8.352245207 + -5.6 Combine like terms: 8.352245207 + -5.6 = 2.752245207 x = 2.752245207 Simplifying x = 2.752245207Subproblem 2
x + 5.6 = -8.352245207 Simplifying x + 5.6 = -8.352245207 Reorder the terms: 5.6 + x = -8.352245207 Solving 5.6 + x = -8.352245207 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 = -8.352245207 + -5.6 Combine like terms: 5.6 + -5.6 = 0.0 0.0 + x = -8.352245207 + -5.6 x = -8.352245207 + -5.6 Combine like terms: -8.352245207 + -5.6 = -13.952245207 x = -13.952245207 Simplifying x = -13.952245207Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.752245207, -13.952245207}
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