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Simplifying 3x2 + 7x + -81 = 0 Reorder the terms: -81 + 7x + 3x2 = 0 Solving -81 + 7x + 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'. -27 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '27' to each side of the equation. -27 + 2.333333333x + 27 + x2 = 0 + 27 Reorder the terms: -27 + 27 + 2.333333333x + x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 2.333333333x + x2 = 0 + 27 2.333333333x + x2 = 0 + 27 Combine like terms: 0 + 27 = 27 2.333333333x + x2 = 27 The x term is 2.333333333x. Take half its coefficient (1.166666667). Square it (1.361111112) and add it to both sides. Add '1.361111112' to each side of the equation. 2.333333333x + 1.361111112 + x2 = 27 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 27 + 1.361111112 Combine like terms: 27 + 1.361111112 = 28.361111112 1.361111112 + 2.333333333x + x2 = 28.361111112 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 28.361111112 Calculate the square root of the right side: 5.325515103 Break this problem into two subproblems by setting (x + 1.166666667) equal to 5.325515103 and -5.325515103.Subproblem 1
x + 1.166666667 = 5.325515103 Simplifying x + 1.166666667 = 5.325515103 Reorder the terms: 1.166666667 + x = 5.325515103 Solving 1.166666667 + x = 5.325515103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 5.325515103 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 5.325515103 + -1.166666667 x = 5.325515103 + -1.166666667 Combine like terms: 5.325515103 + -1.166666667 = 4.158848436 x = 4.158848436 Simplifying x = 4.158848436Subproblem 2
x + 1.166666667 = -5.325515103 Simplifying x + 1.166666667 = -5.325515103 Reorder the terms: 1.166666667 + x = -5.325515103 Solving 1.166666667 + x = -5.325515103 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -5.325515103 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -5.325515103 + -1.166666667 x = -5.325515103 + -1.166666667 Combine like terms: -5.325515103 + -1.166666667 = -6.49218177 x = -6.49218177 Simplifying x = -6.49218177Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.158848436, -6.49218177}
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