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Simplifying 5x2 + -33x + 16 = 0 Reorder the terms: 16 + -33x + 5x2 = 0 Solving 16 + -33x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + -6.6x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + -6.6x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + -6.6x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + -6.6x + x2 = 0 + -3.2 -6.6x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 -6.6x + x2 = -3.2 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 = -3.2 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -3.2 + 10.89 Combine like terms: -3.2 + 10.89 = 7.69 10.89 + -6.6x + x2 = 7.69 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (x + -3.3) equal to 2.773084925 and -2.773084925.Subproblem 1
x + -3.3 = 2.773084925 Simplifying x + -3.3 = 2.773084925 Reorder the terms: -3.3 + x = 2.773084925 Solving -3.3 + x = 2.773084925 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 = 2.773084925 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 2.773084925 + 3.3 x = 2.773084925 + 3.3 Combine like terms: 2.773084925 + 3.3 = 6.073084925 x = 6.073084925 Simplifying x = 6.073084925Subproblem 2
x + -3.3 = -2.773084925 Simplifying x + -3.3 = -2.773084925 Reorder the terms: -3.3 + x = -2.773084925 Solving -3.3 + x = -2.773084925 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 = -2.773084925 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -2.773084925 + 3.3 x = -2.773084925 + 3.3 Combine like terms: -2.773084925 + 3.3 = 0.526915075 x = 0.526915075 Simplifying x = 0.526915075Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.073084925, 0.526915075}
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