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Simplifying 4x2 + -21x + 11 = -8 + 1 Reorder the terms: 11 + -21x + 4x2 = -8 + 1 Combine like terms: -8 + 1 = -7 11 + -21x + 4x2 = -7 Solving 11 + -21x + 4x2 = -7 Solving for variable 'x'. Reorder the terms: 11 + 7 + -21x + 4x2 = -7 + 7 Combine like terms: 11 + 7 = 18 18 + -21x + 4x2 = -7 + 7 Combine like terms: -7 + 7 = 0 18 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 4.5 + -5.25x + x2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + -5.25x + -4.5 + x2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + -5.25x + x2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + -5.25x + x2 = 0 + -4.5 -5.25x + x2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 -5.25x + x2 = -4.5 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = -4.5 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = -4.5 + 6.890625 Combine like terms: -4.5 + 6.890625 = 2.390625 6.890625 + -5.25x + x2 = 2.390625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (x + -2.625) equal to 1.54616461 and -1.54616461.Subproblem 1
x + -2.625 = 1.54616461 Simplifying x + -2.625 = 1.54616461 Reorder the terms: -2.625 + x = 1.54616461 Solving -2.625 + x = 1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 1.54616461 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 1.54616461 + 2.625 x = 1.54616461 + 2.625 Combine like terms: 1.54616461 + 2.625 = 4.17116461 x = 4.17116461 Simplifying x = 4.17116461Subproblem 2
x + -2.625 = -1.54616461 Simplifying x + -2.625 = -1.54616461 Reorder the terms: -2.625 + x = -1.54616461 Solving -2.625 + x = -1.54616461 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -1.54616461 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -1.54616461 + 2.625 x = -1.54616461 + 2.625 Combine like terms: -1.54616461 + 2.625 = 1.07883539 x = 1.07883539 Simplifying x = 1.07883539Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.17116461, 1.07883539}
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