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Simplifying 4x2 + -52x + 33 = 0 Reorder the terms: 33 + -52x + 4x2 = 0 Solving 33 + -52x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 8.25 + -13x + x2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -13x + -8.25 + x2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -13x + x2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -13x + x2 = 0 + -8.25 -13x + x2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -13x + x2 = -8.25 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = -8.25 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -8.25 + 42.25 Combine like terms: -8.25 + 42.25 = 34 42.25 + -13x + x2 = 34 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -6.5) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -6.5 = 5.830951895 Simplifying x + -6.5 = 5.830951895 Reorder the terms: -6.5 + x = 5.830951895 Solving -6.5 + x = 5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 5.830951895 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 5.830951895 + 6.5 x = 5.830951895 + 6.5 Combine like terms: 5.830951895 + 6.5 = 12.330951895 x = 12.330951895 Simplifying x = 12.330951895Subproblem 2
x + -6.5 = -5.830951895 Simplifying x + -6.5 = -5.830951895 Reorder the terms: -6.5 + x = -5.830951895 Solving -6.5 + x = -5.830951895 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -5.830951895 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -5.830951895 + 6.5 x = -5.830951895 + 6.5 Combine like terms: -5.830951895 + 6.5 = 0.669048105 x = 0.669048105 Simplifying x = 0.669048105Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.330951895, 0.669048105}
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