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Simplifying 9x2 + -134x + 8 = 0 Reorder the terms: 8 + -134x + 9x2 = 0 Solving 8 + -134x + 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 + -14.88888889x + x2 = 0 Move the constant term to the right: Add '-0.8888888889' to each side of the equation. 0.8888888889 + -14.88888889x + -0.8888888889 + x2 = 0 + -0.8888888889 Reorder the terms: 0.8888888889 + -0.8888888889 + -14.88888889x + x2 = 0 + -0.8888888889 Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000 0.0000000000 + -14.88888889x + x2 = 0 + -0.8888888889 -14.88888889x + x2 = 0 + -0.8888888889 Combine like terms: 0 + -0.8888888889 = -0.8888888889 -14.88888889x + x2 = -0.8888888889 The x term is -14.88888889x. Take half its coefficient (-7.444444445). Square it (55.41975309) and add it to both sides. Add '55.41975309' to each side of the equation. -14.88888889x + 55.41975309 + x2 = -0.8888888889 + 55.41975309 Reorder the terms: 55.41975309 + -14.88888889x + x2 = -0.8888888889 + 55.41975309 Combine like terms: -0.8888888889 + 55.41975309 = 54.5308642011 55.41975309 + -14.88888889x + x2 = 54.5308642011 Factor a perfect square on the left side: (x + -7.444444445)(x + -7.444444445) = 54.5308642011 Calculate the square root of the right side: 7.384501622 Break this problem into two subproblems by setting (x + -7.444444445) equal to 7.384501622 and -7.384501622.Subproblem 1
x + -7.444444445 = 7.384501622 Simplifying x + -7.444444445 = 7.384501622 Reorder the terms: -7.444444445 + x = 7.384501622 Solving -7.444444445 + x = 7.384501622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.444444445' to each side of the equation. -7.444444445 + 7.444444445 + x = 7.384501622 + 7.444444445 Combine like terms: -7.444444445 + 7.444444445 = 0.000000000 0.000000000 + x = 7.384501622 + 7.444444445 x = 7.384501622 + 7.444444445 Combine like terms: 7.384501622 + 7.444444445 = 14.828946067 x = 14.828946067 Simplifying x = 14.828946067Subproblem 2
x + -7.444444445 = -7.384501622 Simplifying x + -7.444444445 = -7.384501622 Reorder the terms: -7.444444445 + x = -7.384501622 Solving -7.444444445 + x = -7.384501622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.444444445' to each side of the equation. -7.444444445 + 7.444444445 + x = -7.384501622 + 7.444444445 Combine like terms: -7.444444445 + 7.444444445 = 0.000000000 0.000000000 + x = -7.384501622 + 7.444444445 x = -7.384501622 + 7.444444445 Combine like terms: -7.384501622 + 7.444444445 = 0.059942823 x = 0.059942823 Simplifying x = 0.059942823Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.828946067, 0.059942823}
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