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Simplifying X2 + -12X + -80 = 0 Reorder the terms: -80 + -12X + X2 = 0 Solving -80 + -12X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -12X + 80 + X2 = 0 + 80 Reorder the terms: -80 + 80 + -12X + X2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -12X + X2 = 0 + 80 -12X + X2 = 0 + 80 Combine like terms: 0 + 80 = 80 -12X + X2 = 80 The X term is -12X. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12X + 36 + X2 = 80 + 36 Reorder the terms: 36 + -12X + X2 = 80 + 36 Combine like terms: 80 + 36 = 116 36 + -12X + X2 = 116 Factor a perfect square on the left side: (X + -6)(X + -6) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (X + -6) equal to 10.770329614 and -10.770329614.Subproblem 1
X + -6 = 10.770329614 Simplifying X + -6 = 10.770329614 Reorder the terms: -6 + X = 10.770329614 Solving -6 + X = 10.770329614 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = 10.770329614 + 6 Combine like terms: -6 + 6 = 0 0 + X = 10.770329614 + 6 X = 10.770329614 + 6 Combine like terms: 10.770329614 + 6 = 16.770329614 X = 16.770329614 Simplifying X = 16.770329614Subproblem 2
X + -6 = -10.770329614 Simplifying X + -6 = -10.770329614 Reorder the terms: -6 + X = -10.770329614 Solving -6 + X = -10.770329614 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + X = -10.770329614 + 6 Combine like terms: -6 + 6 = 0 0 + X = -10.770329614 + 6 X = -10.770329614 + 6 Combine like terms: -10.770329614 + 6 = -4.770329614 X = -4.770329614 Simplifying X = -4.770329614Solution
The solution to the problem is based on the solutions from the subproblems. X = {16.770329614, -4.770329614}
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