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Simplifying x2 + 96x + -660 = 0 Reorder the terms: -660 + 96x + x2 = 0 Solving -660 + 96x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '660' to each side of the equation. -660 + 96x + 660 + x2 = 0 + 660 Reorder the terms: -660 + 660 + 96x + x2 = 0 + 660 Combine like terms: -660 + 660 = 0 0 + 96x + x2 = 0 + 660 96x + x2 = 0 + 660 Combine like terms: 0 + 660 = 660 96x + x2 = 660 The x term is 96x. Take half its coefficient (48). Square it (2304) and add it to both sides. Add '2304' to each side of the equation. 96x + 2304 + x2 = 660 + 2304 Reorder the terms: 2304 + 96x + x2 = 660 + 2304 Combine like terms: 660 + 2304 = 2964 2304 + 96x + x2 = 2964 Factor a perfect square on the left side: (x + 48)(x + 48) = 2964 Calculate the square root of the right side: 54.442630355 Break this problem into two subproblems by setting (x + 48) equal to 54.442630355 and -54.442630355.Subproblem 1
x + 48 = 54.442630355 Simplifying x + 48 = 54.442630355 Reorder the terms: 48 + x = 54.442630355 Solving 48 + x = 54.442630355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = 54.442630355 + -48 Combine like terms: 48 + -48 = 0 0 + x = 54.442630355 + -48 x = 54.442630355 + -48 Combine like terms: 54.442630355 + -48 = 6.442630355 x = 6.442630355 Simplifying x = 6.442630355Subproblem 2
x + 48 = -54.442630355 Simplifying x + 48 = -54.442630355 Reorder the terms: 48 + x = -54.442630355 Solving 48 + x = -54.442630355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-48' to each side of the equation. 48 + -48 + x = -54.442630355 + -48 Combine like terms: 48 + -48 = 0 0 + x = -54.442630355 + -48 x = -54.442630355 + -48 Combine like terms: -54.442630355 + -48 = -102.442630355 x = -102.442630355 Simplifying x = -102.442630355Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.442630355, -102.442630355}
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