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Simplifying (-1X2) + (12X) + -21 = 0 Reorder the terms: -21 + (12X) + (-1X2) = 0 Solving -21 + (12X) + (-1X2) = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 21 + (-12X) + X2 = 0 Move the constant term to the right: Add '-21' to each side of the equation. 21 + (-12X) + -21 + X2 = 0 + -21 Reorder the terms: 21 + -21 + (-12X) + X2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + (-12X) + X2 = 0 + -21 (-12X) + X2 = 0 + -21 Combine like terms: 0 + -21 = -21 (-12X) + X2 = -21 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 = -21 + 36 Reorder the terms: 36 + (-12X) + X2 = -21 + 36 Combine like terms: -21 + 36 = 15 36 + (-12X) + X2 = 15 Factor a perfect square on the left side: ((X) + -6)((X) + -6) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting ((X) + -6) equal to 3.872983346 and -3.872983346.Subproblem 1
(X) + -6 = 3.872983346 Simplifying (X) + -6 = 3.872983346 X + -6 = 3.872983346 Reorder the terms: -6 + X = 3.872983346 Solving -6 + X = 3.872983346 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 = 3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + X = 3.872983346 + 6 X = 3.872983346 + 6 Combine like terms: 3.872983346 + 6 = 9.872983346 X = 9.872983346 Simplifying X = 9.872983346Subproblem 2
(X) + -6 = -3.872983346 Simplifying (X) + -6 = -3.872983346 X + -6 = -3.872983346 Reorder the terms: -6 + X = -3.872983346 Solving -6 + X = -3.872983346 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 = -3.872983346 + 6 Combine like terms: -6 + 6 = 0 0 + X = -3.872983346 + 6 X = -3.872983346 + 6 Combine like terms: -3.872983346 + 6 = 2.127016654 X = 2.127016654 Simplifying X = 2.127016654Solution
The solution to the problem is based on the solutions from the subproblems. X = {9.872983346, 2.127016654}
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