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Simplifying 21x2 + 6 + 33x = 0 Reorder the terms: 6 + 33x + 21x2 = 0 Solving 6 + 33x + 21x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(2 + 11x + 7x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + 11x + 7x2)' equal to zero and attempt to solve: Simplifying 2 + 11x + 7x2 = 0 Solving 2 + 11x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.2857142857 + 1.571428571x + x2 = 0 Move the constant term to the right: Add '-0.2857142857' to each side of the equation. 0.2857142857 + 1.571428571x + -0.2857142857 + x2 = 0 + -0.2857142857 Reorder the terms: 0.2857142857 + -0.2857142857 + 1.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0.2857142857 + -0.2857142857 = 0.0000000000 0.0000000000 + 1.571428571x + x2 = 0 + -0.2857142857 1.571428571x + x2 = 0 + -0.2857142857 Combine like terms: 0 + -0.2857142857 = -0.2857142857 1.571428571x + x2 = -0.2857142857 The x term is 1.571428571x. Take half its coefficient (0.7857142855). Square it (0.6173469384) and add it to both sides. Add '0.6173469384' to each side of the equation. 1.571428571x + 0.6173469384 + x2 = -0.2857142857 + 0.6173469384 Reorder the terms: 0.6173469384 + 1.571428571x + x2 = -0.2857142857 + 0.6173469384 Combine like terms: -0.2857142857 + 0.6173469384 = 0.3316326527 0.6173469384 + 1.571428571x + x2 = 0.3316326527 Factor a perfect square on the left side: (x + 0.7857142855)(x + 0.7857142855) = 0.3316326527 Calculate the square root of the right side: 0.575875553 Break this problem into two subproblems by setting (x + 0.7857142855) equal to 0.575875553 and -0.575875553.Subproblem 1
x + 0.7857142855 = 0.575875553 Simplifying x + 0.7857142855 = 0.575875553 Reorder the terms: 0.7857142855 + x = 0.575875553 Solving 0.7857142855 + x = 0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = 0.575875553 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = 0.575875553 + -0.7857142855 x = 0.575875553 + -0.7857142855 Combine like terms: 0.575875553 + -0.7857142855 = -0.2098387325 x = -0.2098387325 Simplifying x = -0.2098387325Subproblem 2
x + 0.7857142855 = -0.575875553 Simplifying x + 0.7857142855 = -0.575875553 Reorder the terms: 0.7857142855 + x = -0.575875553 Solving 0.7857142855 + x = -0.575875553 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7857142855' to each side of the equation. 0.7857142855 + -0.7857142855 + x = -0.575875553 + -0.7857142855 Combine like terms: 0.7857142855 + -0.7857142855 = 0.0000000000 0.0000000000 + x = -0.575875553 + -0.7857142855 x = -0.575875553 + -0.7857142855 Combine like terms: -0.575875553 + -0.7857142855 = -1.3615898385 x = -1.3615898385 Simplifying x = -1.3615898385Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.2098387325, -1.3615898385}Solution
x = {-0.2098387325, -1.3615898385}
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