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Simplifying X2 + -6X + -101 = 0 Reorder the terms: -101 + -6X + X2 = 0 Solving -101 + -6X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '101' to each side of the equation. -101 + -6X + 101 + X2 = 0 + 101 Reorder the terms: -101 + 101 + -6X + X2 = 0 + 101 Combine like terms: -101 + 101 = 0 0 + -6X + X2 = 0 + 101 -6X + X2 = 0 + 101 Combine like terms: 0 + 101 = 101 -6X + X2 = 101 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = 101 + 9 Reorder the terms: 9 + -6X + X2 = 101 + 9 Combine like terms: 101 + 9 = 110 9 + -6X + X2 = 110 Factor a perfect square on the left side: (X + -3)(X + -3) = 110 Calculate the square root of the right side: 10.488088482 Break this problem into two subproblems by setting (X + -3) equal to 10.488088482 and -10.488088482.Subproblem 1
X + -3 = 10.488088482 Simplifying X + -3 = 10.488088482 Reorder the terms: -3 + X = 10.488088482 Solving -3 + X = 10.488088482 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 10.488088482 + 3 Combine like terms: -3 + 3 = 0 0 + X = 10.488088482 + 3 X = 10.488088482 + 3 Combine like terms: 10.488088482 + 3 = 13.488088482 X = 13.488088482 Simplifying X = 13.488088482Subproblem 2
X + -3 = -10.488088482 Simplifying X + -3 = -10.488088482 Reorder the terms: -3 + X = -10.488088482 Solving -3 + X = -10.488088482 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -10.488088482 + 3 Combine like terms: -3 + 3 = 0 0 + X = -10.488088482 + 3 X = -10.488088482 + 3 Combine like terms: -10.488088482 + 3 = -7.488088482 X = -7.488088482 Simplifying X = -7.488088482Solution
The solution to the problem is based on the solutions from the subproblems. X = {13.488088482, -7.488088482}
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