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Simplifying 3x2 + 16x + -84 = 0 Reorder the terms: -84 + 16x + 3x2 = 0 Solving -84 + 16x + 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'. -28 + 5.333333333x + x2 = 0 Move the constant term to the right: Add '28' to each side of the equation. -28 + 5.333333333x + 28 + x2 = 0 + 28 Reorder the terms: -28 + 28 + 5.333333333x + x2 = 0 + 28 Combine like terms: -28 + 28 = 0 0 + 5.333333333x + x2 = 0 + 28 5.333333333x + x2 = 0 + 28 Combine like terms: 0 + 28 = 28 5.333333333x + x2 = 28 The x term is 5.333333333x. Take half its coefficient (2.666666667). Square it (7.111111113) and add it to both sides. Add '7.111111113' to each side of the equation. 5.333333333x + 7.111111113 + x2 = 28 + 7.111111113 Reorder the terms: 7.111111113 + 5.333333333x + x2 = 28 + 7.111111113 Combine like terms: 28 + 7.111111113 = 35.111111113 7.111111113 + 5.333333333x + x2 = 35.111111113 Factor a perfect square on the left side: (x + 2.666666667)(x + 2.666666667) = 35.111111113 Calculate the square root of the right side: 5.925462945 Break this problem into two subproblems by setting (x + 2.666666667) equal to 5.925462945 and -5.925462945.Subproblem 1
x + 2.666666667 = 5.925462945 Simplifying x + 2.666666667 = 5.925462945 Reorder the terms: 2.666666667 + x = 5.925462945 Solving 2.666666667 + x = 5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = 5.925462945 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = 5.925462945 + -2.666666667 x = 5.925462945 + -2.666666667 Combine like terms: 5.925462945 + -2.666666667 = 3.258796278 x = 3.258796278 Simplifying x = 3.258796278Subproblem 2
x + 2.666666667 = -5.925462945 Simplifying x + 2.666666667 = -5.925462945 Reorder the terms: 2.666666667 + x = -5.925462945 Solving 2.666666667 + x = -5.925462945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.666666667' to each side of the equation. 2.666666667 + -2.666666667 + x = -5.925462945 + -2.666666667 Combine like terms: 2.666666667 + -2.666666667 = 0.000000000 0.000000000 + x = -5.925462945 + -2.666666667 x = -5.925462945 + -2.666666667 Combine like terms: -5.925462945 + -2.666666667 = -8.592129612 x = -8.592129612 Simplifying x = -8.592129612Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.258796278, -8.592129612}
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