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Simplifying 4X2 + -16X + -11 = 0 Reorder the terms: -11 + -16X + 4X2 = 0 Solving -11 + -16X + 4X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -4X + X2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -4X + 2.75 + X2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -4X + X2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -4X + X2 = 0 + 2.75 -4X + X2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -4X + X2 = 2.75 The X term is -4X. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4X + 4 + X2 = 2.75 + 4 Reorder the terms: 4 + -4X + X2 = 2.75 + 4 Combine like terms: 2.75 + 4 = 6.75 4 + -4X + X2 = 6.75 Factor a perfect square on the left side: (X + -2)(X + -2) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (X + -2) equal to 2.598076211 and -2.598076211.Subproblem 1
X + -2 = 2.598076211 Simplifying X + -2 = 2.598076211 Reorder the terms: -2 + X = 2.598076211 Solving -2 + X = 2.598076211 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = 2.598076211 + 2 Combine like terms: -2 + 2 = 0 0 + X = 2.598076211 + 2 X = 2.598076211 + 2 Combine like terms: 2.598076211 + 2 = 4.598076211 X = 4.598076211 Simplifying X = 4.598076211Subproblem 2
X + -2 = -2.598076211 Simplifying X + -2 = -2.598076211 Reorder the terms: -2 + X = -2.598076211 Solving -2 + X = -2.598076211 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + X = -2.598076211 + 2 Combine like terms: -2 + 2 = 0 0 + X = -2.598076211 + 2 X = -2.598076211 + 2 Combine like terms: -2.598076211 + 2 = -0.598076211 X = -0.598076211 Simplifying X = -0.598076211Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.598076211, -0.598076211}
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