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Simplifying x2 + -7x + -12 = 180 Reorder the terms: -12 + -7x + x2 = 180 Solving -12 + -7x + x2 = 180 Solving for variable 'x'. Reorder the terms: -12 + -180 + -7x + x2 = 180 + -180 Combine like terms: -12 + -180 = -192 -192 + -7x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -192 + -7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + -7x + 192 + x2 = 0 + 192 Reorder the terms: -192 + 192 + -7x + x2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + -7x + x2 = 0 + 192 -7x + x2 = 0 + 192 Combine like terms: 0 + 192 = 192 -7x + x2 = 192 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 192 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 192 + 12.25 Combine like terms: 192 + 12.25 = 204.25 12.25 + -7x + x2 = 204.25 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 204.25 Calculate the square root of the right side: 14.291605928 Break this problem into two subproblems by setting (x + -3.5) equal to 14.291605928 and -14.291605928.Subproblem 1
x + -3.5 = 14.291605928 Simplifying x + -3.5 = 14.291605928 Reorder the terms: -3.5 + x = 14.291605928 Solving -3.5 + x = 14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 14.291605928 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 14.291605928 + 3.5 x = 14.291605928 + 3.5 Combine like terms: 14.291605928 + 3.5 = 17.791605928 x = 17.791605928 Simplifying x = 17.791605928Subproblem 2
x + -3.5 = -14.291605928 Simplifying x + -3.5 = -14.291605928 Reorder the terms: -3.5 + x = -14.291605928 Solving -3.5 + x = -14.291605928 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -14.291605928 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -14.291605928 + 3.5 x = -14.291605928 + 3.5 Combine like terms: -14.291605928 + 3.5 = -10.791605928 x = -10.791605928 Simplifying x = -10.791605928Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.791605928, -10.791605928}
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