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Simplifying 3x2 + 21x + 16 = 0 Reorder the terms: 16 + 21x + 3x2 = 0 Solving 16 + 21x + 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 + 7x + x2 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + 7x + -5.333333333 + x2 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + 7x + x2 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + 7x + x2 = 0 + -5.333333333 7x + x2 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 7x + x2 = -5.333333333 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -5.333333333 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -5.333333333 + 12.25 Combine like terms: -5.333333333 + 12.25 = 6.916666667 12.25 + 7x + x2 = 6.916666667 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 6.916666667 Calculate the square root of the right side: 2.62995564 Break this problem into two subproblems by setting (x + 3.5) equal to 2.62995564 and -2.62995564.Subproblem 1
x + 3.5 = 2.62995564 Simplifying x + 3.5 = 2.62995564 Reorder the terms: 3.5 + x = 2.62995564 Solving 3.5 + x = 2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.62995564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.62995564 + -3.5 x = 2.62995564 + -3.5 Combine like terms: 2.62995564 + -3.5 = -0.87004436 x = -0.87004436 Simplifying x = -0.87004436Subproblem 2
x + 3.5 = -2.62995564 Simplifying x + 3.5 = -2.62995564 Reorder the terms: 3.5 + x = -2.62995564 Solving 3.5 + x = -2.62995564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.62995564 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.62995564 + -3.5 x = -2.62995564 + -3.5 Combine like terms: -2.62995564 + -3.5 = -6.12995564 x = -6.12995564 Simplifying x = -6.12995564Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.87004436, -6.12995564}
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