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Simplifying 4x2 + -27x + 11 = 6x + 6 Reorder the terms: 11 + -27x + 4x2 = 6x + 6 Reorder the terms: 11 + -27x + 4x2 = 6 + 6x Solving 11 + -27x + 4x2 = 6 + 6x Solving for variable 'x'. Reorder the terms: 11 + -6 + -27x + -6x + 4x2 = 6 + 6x + -6 + -6x Combine like terms: 11 + -6 = 5 5 + -27x + -6x + 4x2 = 6 + 6x + -6 + -6x Combine like terms: -27x + -6x = -33x 5 + -33x + 4x2 = 6 + 6x + -6 + -6x Reorder the terms: 5 + -33x + 4x2 = 6 + -6 + 6x + -6x Combine like terms: 6 + -6 = 0 5 + -33x + 4x2 = 0 + 6x + -6x 5 + -33x + 4x2 = 6x + -6x Combine like terms: 6x + -6x = 0 5 + -33x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + -8.25x + x2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + -8.25x + -1.25 + x2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + -8.25x + x2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + -8.25x + x2 = 0 + -1.25 -8.25x + x2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 -8.25x + x2 = -1.25 The x term is -8.25x. Take half its coefficient (-4.125). Square it (17.015625) and add it to both sides. Add '17.015625' to each side of the equation. -8.25x + 17.015625 + x2 = -1.25 + 17.015625 Reorder the terms: 17.015625 + -8.25x + x2 = -1.25 + 17.015625 Combine like terms: -1.25 + 17.015625 = 15.765625 17.015625 + -8.25x + x2 = 15.765625 Factor a perfect square on the left side: (x + -4.125)(x + -4.125) = 15.765625 Calculate the square root of the right side: 3.970595044 Break this problem into two subproblems by setting (x + -4.125) equal to 3.970595044 and -3.970595044.Subproblem 1
x + -4.125 = 3.970595044 Simplifying x + -4.125 = 3.970595044 Reorder the terms: -4.125 + x = 3.970595044 Solving -4.125 + x = 3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = 3.970595044 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = 3.970595044 + 4.125 x = 3.970595044 + 4.125 Combine like terms: 3.970595044 + 4.125 = 8.095595044 x = 8.095595044 Simplifying x = 8.095595044Subproblem 2
x + -4.125 = -3.970595044 Simplifying x + -4.125 = -3.970595044 Reorder the terms: -4.125 + x = -3.970595044 Solving -4.125 + x = -3.970595044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.125' to each side of the equation. -4.125 + 4.125 + x = -3.970595044 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + x = -3.970595044 + 4.125 x = -3.970595044 + 4.125 Combine like terms: -3.970595044 + 4.125 = 0.154404956 x = 0.154404956 Simplifying x = 0.154404956Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.095595044, 0.154404956}
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