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Simplifying 4X2 + -11X = 3 + -6X Reorder the terms: -11X + 4X2 = 3 + -6X Solving -11X + 4X2 = 3 + -6X Solving for variable 'X'. Reorder the terms: -3 + -11X + 6X + 4X2 = 3 + -6X + -3 + 6X Combine like terms: -11X + 6X = -5X -3 + -5X + 4X2 = 3 + -6X + -3 + 6X Reorder the terms: -3 + -5X + 4X2 = 3 + -3 + -6X + 6X Combine like terms: 3 + -3 = 0 -3 + -5X + 4X2 = 0 + -6X + 6X -3 + -5X + 4X2 = -6X + 6X Combine like terms: -6X + 6X = 0 -3 + -5X + 4X2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + -1.25X + X2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -1.25X + 0.75 + X2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -1.25X + X2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -1.25X + X2 = 0 + 0.75 -1.25X + X2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -1.25X + X2 = 0.75 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 = 0.75 + 0.390625 Reorder the terms: 0.390625 + -1.25X + X2 = 0.75 + 0.390625 Combine like terms: 0.75 + 0.390625 = 1.140625 0.390625 + -1.25X + X2 = 1.140625 Factor a perfect square on the left side: (X + -0.625)(X + -0.625) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (X + -0.625) equal to 1.068000468 and -1.068000468.Subproblem 1
X + -0.625 = 1.068000468 Simplifying X + -0.625 = 1.068000468 Reorder the terms: -0.625 + X = 1.068000468 Solving -0.625 + X = 1.068000468 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 = 1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + X = 1.068000468 + 0.625 X = 1.068000468 + 0.625 Combine like terms: 1.068000468 + 0.625 = 1.693000468 X = 1.693000468 Simplifying X = 1.693000468Subproblem 2
X + -0.625 = -1.068000468 Simplifying X + -0.625 = -1.068000468 Reorder the terms: -0.625 + X = -1.068000468 Solving -0.625 + X = -1.068000468 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 = -1.068000468 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + X = -1.068000468 + 0.625 X = -1.068000468 + 0.625 Combine like terms: -1.068000468 + 0.625 = -0.443000468 X = -0.443000468 Simplifying X = -0.443000468Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.693000468, -0.443000468}
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