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Simplifying 3x2 + -33x + 9 = 1 Reorder the terms: 9 + -33x + 3x2 = 1 Solving 9 + -33x + 3x2 = 1 Solving for variable 'x'. Reorder the terms: 9 + -1 + -33x + 3x2 = 1 + -1 Combine like terms: 9 + -1 = 8 8 + -33x + 3x2 = 1 + -1 Combine like terms: 1 + -1 = 0 8 + -33x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 2.666666667 + -11x + x2 = 0 Move the constant term to the right: Add '-2.666666667' to each side of the equation. 2.666666667 + -11x + -2.666666667 + x2 = 0 + -2.666666667 Reorder the terms: 2.666666667 + -2.666666667 + -11x + x2 = 0 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + -11x + x2 = 0 + -2.666666667 -11x + x2 = 0 + -2.666666667 Combine like terms: 0 + -2.666666667 = -2.666666667 -11x + x2 = -2.666666667 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = -2.666666667 + 30.25 Reorder the terms: 30.25 + -11x + x2 = -2.666666667 + 30.25 Combine like terms: -2.666666667 + 30.25 = 27.583333333 30.25 + -11x + x2 = 27.583333333 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 27.583333333 Calculate the square root of the right side: 5.251983752 Break this problem into two subproblems by setting (x + -5.5) equal to 5.251983752 and -5.251983752.Subproblem 1
x + -5.5 = 5.251983752 Simplifying x + -5.5 = 5.251983752 Reorder the terms: -5.5 + x = 5.251983752 Solving -5.5 + x = 5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 5.251983752 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 5.251983752 + 5.5 x = 5.251983752 + 5.5 Combine like terms: 5.251983752 + 5.5 = 10.751983752 x = 10.751983752 Simplifying x = 10.751983752Subproblem 2
x + -5.5 = -5.251983752 Simplifying x + -5.5 = -5.251983752 Reorder the terms: -5.5 + x = -5.251983752 Solving -5.5 + x = -5.251983752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -5.251983752 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -5.251983752 + 5.5 x = -5.251983752 + 5.5 Combine like terms: -5.251983752 + 5.5 = 0.248016248 x = 0.248016248 Simplifying x = 0.248016248Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.751983752, 0.248016248}
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