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Simplifying -3x2 + 18x + 16 = 0 Reorder the terms: 16 + 18x + -3x2 = 0 Solving 16 + 18x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5.333333333 + -6x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -6x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -6x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -6x + x2 = 0 + 5.333333333 -6x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -6x + x2 = 5.333333333 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 5.333333333 + 9 Reorder the terms: 9 + -6x + x2 = 5.333333333 + 9 Combine like terms: 5.333333333 + 9 = 14.333333333 9 + -6x + x2 = 14.333333333 Factor a perfect square on the left side: (x + -3)(x + -3) = 14.333333333 Calculate the square root of the right side: 3.785938897 Break this problem into two subproblems by setting (x + -3) equal to 3.785938897 and -3.785938897.Subproblem 1
x + -3 = 3.785938897 Simplifying x + -3 = 3.785938897 Reorder the terms: -3 + x = 3.785938897 Solving -3 + x = 3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 3.785938897 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.785938897 + 3 x = 3.785938897 + 3 Combine like terms: 3.785938897 + 3 = 6.785938897 x = 6.785938897 Simplifying x = 6.785938897Subproblem 2
x + -3 = -3.785938897 Simplifying x + -3 = -3.785938897 Reorder the terms: -3 + x = -3.785938897 Solving -3 + x = -3.785938897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -3.785938897 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.785938897 + 3 x = -3.785938897 + 3 Combine like terms: -3.785938897 + 3 = -0.785938897 x = -0.785938897 Simplifying x = -0.785938897Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.785938897, -0.785938897}
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