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Simplifying 0 = x2 + -6.6x + 8 Reorder the terms: 0 = 8 + -6.6x + x2 Solving 0 = 8 + -6.6x + x2 Solving for variable 'x'. Combine like terms: 0 + -8 = -8 -8 + 6.6x + -1x2 = 8 + -6.6x + x2 + -8 + 6.6x + -1x2 Reorder the terms: -8 + 6.6x + -1x2 = 8 + -8 + -6.6x + 6.6x + x2 + -1x2 Combine like terms: 8 + -8 = 0 -8 + 6.6x + -1x2 = 0 + -6.6x + 6.6x + x2 + -1x2 -8 + 6.6x + -1x2 = -6.6x + 6.6x + x2 + -1x2 Combine like terms: -6.6x + 6.6x = 0.0 -8 + 6.6x + -1x2 = 0.0 + x2 + -1x2 -8 + 6.6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8 + 6.6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -6.6x + x2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -6.6x + -8 + x2 = 0 + -8 Reorder the terms: 8 + -8 + -6.6x + x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -6.6x + x2 = 0 + -8 -6.6x + x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -6.6x + x2 = -8 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -8 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -8 + 10.89 Combine like terms: -8 + 10.89 = 2.89 10.89 + -6.6x + x2 = 2.89 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 2.89 Calculate the square root of the right side: 1.7 Break this problem into two subproblems by setting (x + -3.3) equal to 1.7 and -1.7.Subproblem 1
x + -3.3 = 1.7 Simplifying x + -3.3 = 1.7 Reorder the terms: -3.3 + x = 1.7 Solving -3.3 + x = 1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 1.7 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 1.7 + 3.3 x = 1.7 + 3.3 Combine like terms: 1.7 + 3.3 = 5 x = 5 Simplifying x = 5Subproblem 2
x + -3.3 = -1.7 Simplifying x + -3.3 = -1.7 Reorder the terms: -3.3 + x = -1.7 Solving -3.3 + x = -1.7 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -1.7 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -1.7 + 3.3 x = -1.7 + 3.3 Combine like terms: -1.7 + 3.3 = 1.6 x = 1.6 Simplifying x = 1.6Solution
The solution to the problem is based on the solutions from the subproblems. x = {5, 1.6}
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