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Simplifying x2 = 12 + -123x Solving x2 = 12 + -123x Solving for variable 'x'. Reorder the terms: -12 + 123x + x2 = 12 + -123x + -12 + 123x Reorder the terms: -12 + 123x + x2 = 12 + -12 + -123x + 123x Combine like terms: 12 + -12 = 0 -12 + 123x + x2 = 0 + -123x + 123x -12 + 123x + x2 = -123x + 123x Combine like terms: -123x + 123x = 0 -12 + 123x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '12' to each side of the equation. -12 + 123x + 12 + x2 = 0 + 12 Reorder the terms: -12 + 12 + 123x + x2 = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 123x + x2 = 0 + 12 123x + x2 = 0 + 12 Combine like terms: 0 + 12 = 12 123x + x2 = 12 The x term is 123x. Take half its coefficient (61.5). Square it (3782.25) and add it to both sides. Add '3782.25' to each side of the equation. 123x + 3782.25 + x2 = 12 + 3782.25 Reorder the terms: 3782.25 + 123x + x2 = 12 + 3782.25 Combine like terms: 12 + 3782.25 = 3794.25 3782.25 + 123x + x2 = 3794.25 Factor a perfect square on the left side: (x + 61.5)(x + 61.5) = 3794.25 Calculate the square root of the right side: 61.597483715 Break this problem into two subproblems by setting (x + 61.5) equal to 61.597483715 and -61.597483715.Subproblem 1
x + 61.5 = 61.597483715 Simplifying x + 61.5 = 61.597483715 Reorder the terms: 61.5 + x = 61.597483715 Solving 61.5 + x = 61.597483715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.5' to each side of the equation. 61.5 + -61.5 + x = 61.597483715 + -61.5 Combine like terms: 61.5 + -61.5 = 0.0 0.0 + x = 61.597483715 + -61.5 x = 61.597483715 + -61.5 Combine like terms: 61.597483715 + -61.5 = 0.097483715 x = 0.097483715 Simplifying x = 0.097483715Subproblem 2
x + 61.5 = -61.597483715 Simplifying x + 61.5 = -61.597483715 Reorder the terms: 61.5 + x = -61.597483715 Solving 61.5 + x = -61.597483715 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-61.5' to each side of the equation. 61.5 + -61.5 + x = -61.597483715 + -61.5 Combine like terms: 61.5 + -61.5 = 0.0 0.0 + x = -61.597483715 + -61.5 x = -61.597483715 + -61.5 Combine like terms: -61.597483715 + -61.5 = -123.097483715 x = -123.097483715 Simplifying x = -123.097483715Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.097483715, -123.097483715}
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