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Simplifying 9x2 + 21x + -18 = 8 Reorder the terms: -18 + 21x + 9x2 = 8 Solving -18 + 21x + 9x2 = 8 Solving for variable 'x'. Reorder the terms: -18 + -8 + 21x + 9x2 = 8 + -8 Combine like terms: -18 + -8 = -26 -26 + 21x + 9x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -26 + 21x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.888888889 + 2.333333333x + x2 = 0 Move the constant term to the right: Add '2.888888889' to each side of the equation. -2.888888889 + 2.333333333x + 2.888888889 + x2 = 0 + 2.888888889 Reorder the terms: -2.888888889 + 2.888888889 + 2.333333333x + x2 = 0 + 2.888888889 Combine like terms: -2.888888889 + 2.888888889 = 0.000000000 0.000000000 + 2.333333333x + x2 = 0 + 2.888888889 2.333333333x + x2 = 0 + 2.888888889 Combine like terms: 0 + 2.888888889 = 2.888888889 2.333333333x + x2 = 2.888888889 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 = 2.888888889 + 1.361111112 Reorder the terms: 1.361111112 + 2.333333333x + x2 = 2.888888889 + 1.361111112 Combine like terms: 2.888888889 + 1.361111112 = 4.250000001 1.361111112 + 2.333333333x + x2 = 4.250000001 Factor a perfect square on the left side: (x + 1.166666667)(x + 1.166666667) = 4.250000001 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (x + 1.166666667) equal to 2.061552813 and -2.061552813.Subproblem 1
x + 1.166666667 = 2.061552813 Simplifying x + 1.166666667 = 2.061552813 Reorder the terms: 1.166666667 + x = 2.061552813 Solving 1.166666667 + x = 2.061552813 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 = 2.061552813 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 2.061552813 + -1.166666667 x = 2.061552813 + -1.166666667 Combine like terms: 2.061552813 + -1.166666667 = 0.894886146 x = 0.894886146 Simplifying x = 0.894886146Subproblem 2
x + 1.166666667 = -2.061552813 Simplifying x + 1.166666667 = -2.061552813 Reorder the terms: 1.166666667 + x = -2.061552813 Solving 1.166666667 + x = -2.061552813 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 = -2.061552813 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -2.061552813 + -1.166666667 x = -2.061552813 + -1.166666667 Combine like terms: -2.061552813 + -1.166666667 = -3.22821948 x = -3.22821948 Simplifying x = -3.22821948Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.894886146, -3.22821948}
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