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Simplifying 9x2 + 21x + 8 = 0 Reorder the terms: 8 + 21x + 9x2 = 0 Solving 8 + 21x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.8888888889 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + 2.333333333x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + 2.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + 2.333333333x + x2 = 0 + -0.8888888889 2.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 2.333333333x + x2 = -0.8888888889 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 = -0.8888888889 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = -0.8888888889 + 1.361111112 Combine like terms: -0.8888888889 + 1.361111112 = 0.4722222231 1.361111112 + 2.333333333x + x2 = 0.4722222231 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 0.4722222231 Calculate the square root of the right side: 0.687184272 Break this problem into two subproblems by setting (x + 1.166666667) equal to 0.687184272 and -0.687184272.Subproblem 1
x + 1.166666667 = 0.687184272 Simplifying x + 1.166666667 = 0.687184272 Reorder the terms: 1.166666667 + x = 0.687184272 Solving 1.166666667 + x = 0.687184272 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 = 0.687184272 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 0.687184272 + -1.166666667 x = 0.687184272 + -1.166666667 Combine like terms: 0.687184272 + -1.166666667 = -0.479482395 x = -0.479482395 Simplifying x = -0.479482395Subproblem 2
x + 1.166666667 = -0.687184272 Simplifying x + 1.166666667 = -0.687184272 Reorder the terms: 1.166666667 + x = -0.687184272 Solving 1.166666667 + x = -0.687184272 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 = -0.687184272 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -0.687184272 + -1.166666667 x = -0.687184272 + -1.166666667 Combine like terms: -0.687184272 + -1.166666667 = -1.853850939 x = -1.853850939 Simplifying x = -1.853850939Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.479482395, -1.853850939}
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