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Simplifying 4X2 + -5X + -11 = 0 Reorder the terms: -11 + -5X + 4X2 = 0 Solving -11 + -5X + 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 + -1.25X + X2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -1.25X + 2.75 + X2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -1.25X + X2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -1.25X + X2 = 0 + 2.75 -1.25X + X2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -1.25X + X2 = 2.75 The X term is -1.25X. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25X + 0.390625 + X2 = 2.75 + 0.390625 Reorder the terms: 0.390625 + -1.25X + X2 = 2.75 + 0.390625 Combine like terms: 2.75 + 0.390625 = 3.140625 0.390625 + -1.25X + X2 = 3.140625 Factor a perfect square on the left side: (X + -0.625)(X + -0.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (X + -0.625) equal to 1.77218086 and -1.77218086.Subproblem 1
X + -0.625 = 1.77218086 Simplifying X + -0.625 = 1.77218086 Reorder the terms: -0.625 + X = 1.77218086 Solving -0.625 + X = 1.77218086 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + X = 1.77218086 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + X = 1.77218086 + 0.625 X = 1.77218086 + 0.625 Combine like terms: 1.77218086 + 0.625 = 2.39718086 X = 2.39718086 Simplifying X = 2.39718086Subproblem 2
X + -0.625 = -1.77218086 Simplifying X + -0.625 = -1.77218086 Reorder the terms: -0.625 + X = -1.77218086 Solving -0.625 + X = -1.77218086 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + X = -1.77218086 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + X = -1.77218086 + 0.625 X = -1.77218086 + 0.625 Combine like terms: -1.77218086 + 0.625 = -1.14718086 X = -1.14718086 Simplifying X = -1.14718086Solution
The solution to the problem is based on the solutions from the subproblems. X = {2.39718086, -1.14718086}
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