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Simplifying X2 + -12X = 100 Reorder the terms: -12X + X2 = 100 Solving -12X + X2 = 100 Solving for variable 'X'. Reorder the terms: -100 + -12X + X2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + -12X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -12X + 100 + X2 = 0 + 100 Reorder the terms: -100 + 100 + -12X + X2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -12X + X2 = 0 + 100 -12X + X2 = 0 + 100 Combine like terms: 0 + 100 = 100 -12X + X2 = 100 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 = 100 + 36 Reorder the terms: 36 + -12X + X2 = 100 + 36 Combine like terms: 100 + 36 = 136 36 + -12X + X2 = 136 Factor a perfect square on the left side: (X + -6)(X + -6) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (X + -6) equal to 11.66190379 and -11.66190379.Subproblem 1
X + -6 = 11.66190379 Simplifying X + -6 = 11.66190379 Reorder the terms: -6 + X = 11.66190379 Solving -6 + X = 11.66190379 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 = 11.66190379 + 6 Combine like terms: -6 + 6 = 0 0 + X = 11.66190379 + 6 X = 11.66190379 + 6 Combine like terms: 11.66190379 + 6 = 17.66190379 X = 17.66190379 Simplifying X = 17.66190379Subproblem 2
X + -6 = -11.66190379 Simplifying X + -6 = -11.66190379 Reorder the terms: -6 + X = -11.66190379 Solving -6 + X = -11.66190379 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 = -11.66190379 + 6 Combine like terms: -6 + 6 = 0 0 + X = -11.66190379 + 6 X = -11.66190379 + 6 Combine like terms: -11.66190379 + 6 = -5.66190379 X = -5.66190379 Simplifying X = -5.66190379Solution
The solution to the problem is based on the solutions from the subproblems. X = {17.66190379, -5.66190379}
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