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Simplifying 9x2 + -9x + 4 = 21x Reorder the terms: 4 + -9x + 9x2 = 21x Solving 4 + -9x + 9x2 = 21x Solving for variable 'x'. Reorder the terms: 4 + -9x + -21x + 9x2 = 21x + -21x Combine like terms: -9x + -21x = -30x 4 + -30x + 9x2 = 21x + -21x Combine like terms: 21x + -21x = 0 4 + -30x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.4444444444 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-0.4444444444' to each side of the equation. 0.4444444444 + -3.333333333x + -0.4444444444 + x2 = 0 + -0.4444444444 Reorder the terms: 0.4444444444 + -0.4444444444 + -3.333333333x + x2 = 0 + -0.4444444444 Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000 0.0000000000 + -3.333333333x + x2 = 0 + -0.4444444444 -3.333333333x + x2 = 0 + -0.4444444444 Combine like terms: 0 + -0.4444444444 = -0.4444444444 -3.333333333x + x2 = -0.4444444444 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = -0.4444444444 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -0.4444444444 + 2.777777779 Combine like terms: -0.4444444444 + 2.777777779 = 2.3333333346 2.777777779 + -3.333333333x + x2 = 2.3333333346 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 2.3333333346 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -1.666666667) equal to 1.527525232 and -1.527525232.Subproblem 1
x + -1.666666667 = 1.527525232 Simplifying x + -1.666666667 = 1.527525232 Reorder the terms: -1.666666667 + x = 1.527525232 Solving -1.666666667 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 1.527525232 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 1.527525232 + 1.666666667 x = 1.527525232 + 1.666666667 Combine like terms: 1.527525232 + 1.666666667 = 3.194191899 x = 3.194191899 Simplifying x = 3.194191899Subproblem 2
x + -1.666666667 = -1.527525232 Simplifying x + -1.666666667 = -1.527525232 Reorder the terms: -1.666666667 + x = -1.527525232 Solving -1.666666667 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -1.527525232 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -1.527525232 + 1.666666667 x = -1.527525232 + 1.666666667 Combine like terms: -1.527525232 + 1.666666667 = 0.139141435 x = 0.139141435 Simplifying x = 0.139141435Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.194191899, 0.139141435}
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