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Simplifying 133 = 3x2 + 3x + 1 Reorder the terms: 133 = 1 + 3x + 3x2 Solving 133 = 1 + 3x + 3x2 Solving for variable 'x'. Combine like terms: 133 + -1 = 132 132 + -3x + -3x2 = 1 + 3x + 3x2 + -1 + -3x + -3x2 Reorder the terms: 132 + -3x + -3x2 = 1 + -1 + 3x + -3x + 3x2 + -3x2 Combine like terms: 1 + -1 = 0 132 + -3x + -3x2 = 0 + 3x + -3x + 3x2 + -3x2 132 + -3x + -3x2 = 3x + -3x + 3x2 + -3x2 Combine like terms: 3x + -3x = 0 132 + -3x + -3x2 = 0 + 3x2 + -3x2 132 + -3x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 132 + -3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(44 + -1x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(44 + -1x + -1x2)' equal to zero and attempt to solve: Simplifying 44 + -1x + -1x2 = 0 Solving 44 + -1x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -44 + x + x2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + x + 44 + x2 = 0 + 44 Reorder the terms: -44 + 44 + x + x2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + x + x2 = 0 + 44 x + x2 = 0 + 44 Combine like terms: 0 + 44 = 44 x + x2 = 44 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 44 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 44 + 0.25 Combine like terms: 44 + 0.25 = 44.25 1.25 + x2 = 44.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 0.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 0.5 = 6.652067348 Simplifying x + 0.5 = 6.652067348 Reorder the terms: 0.5 + x = 6.652067348 Solving 0.5 + x = 6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.652067348 + -0.5 x = 6.652067348 + -0.5 Combine like terms: 6.652067348 + -0.5 = 6.152067348 x = 6.152067348 Simplifying x = 6.152067348Subproblem 2
x + 0.5 = -6.652067348 Simplifying x + 0.5 = -6.652067348 Reorder the terms: 0.5 + x = -6.652067348 Solving 0.5 + x = -6.652067348 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -6.652067348 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.652067348 + -0.5 x = -6.652067348 + -0.5 Combine like terms: -6.652067348 + -0.5 = -7.152067348 x = -7.152067348 Simplifying x = -7.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.152067348, -7.152067348}Solution
x = {6.152067348, -7.152067348}
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