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Simplifying 9x2 + -84x + 8 = 0 Reorder the terms: 8 + -84x + 9x2 = 0 Solving 8 + -84x + 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 + -9.333333333x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -9.333333333x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -9.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -9.333333333x + x2 = 0 + -0.8888888889 -9.333333333x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -9.333333333x + x2 = -0.8888888889 The x term is -9.333333333x. Take half its coefficient (-4.666666667). Square it (21.77777778) and add it to both sides. Add '21.77777778' to each side of the equation. -9.333333333x + 21.77777778 + x2 = -0.8888888889 + 21.77777778 Reorder the terms: 21.77777778 + -9.333333333x + x2 = -0.8888888889 + 21.77777778 Combine like terms: -0.8888888889 + 21.77777778 = 20.8888888911 21.77777778 + -9.333333333x + x2 = 20.8888888911 Factor a perfect square on the left side: (x + -4.666666667)(x + -4.666666667) = 20.8888888911 Calculate the square root of the right side: 4.570436401 Break this problem into two subproblems by setting (x + -4.666666667) equal to 4.570436401 and -4.570436401.Subproblem 1
x + -4.666666667 = 4.570436401 Simplifying x + -4.666666667 = 4.570436401 Reorder the terms: -4.666666667 + x = 4.570436401 Solving -4.666666667 + x = 4.570436401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = 4.570436401 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = 4.570436401 + 4.666666667 x = 4.570436401 + 4.666666667 Combine like terms: 4.570436401 + 4.666666667 = 9.237103068 x = 9.237103068 Simplifying x = 9.237103068Subproblem 2
x + -4.666666667 = -4.570436401 Simplifying x + -4.666666667 = -4.570436401 Reorder the terms: -4.666666667 + x = -4.570436401 Solving -4.666666667 + x = -4.570436401 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.666666667' to each side of the equation. -4.666666667 + 4.666666667 + x = -4.570436401 + 4.666666667 Combine like terms: -4.666666667 + 4.666666667 = 0.000000000 0.000000000 + x = -4.570436401 + 4.666666667 x = -4.570436401 + 4.666666667 Combine like terms: -4.570436401 + 4.666666667 = 0.096230266 x = 0.096230266 Simplifying x = 0.096230266Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.237103068, 0.096230266}
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