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Simplifying 9x2 + 62x + 80 = 0 Reorder the terms: 80 + 62x + 9x2 = 0 Solving 80 + 62x + 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'. 8.888888889 + 6.888888889x + x2 = 0 Move the constant term to the right: Add '-8.888888889' to each side of the equation. 8.888888889 + 6.888888889x + -8.888888889 + x2 = 0 + -8.888888889 Reorder the terms: 8.888888889 + -8.888888889 + 6.888888889x + x2 = 0 + -8.888888889 Combine like terms: 8.888888889 + -8.888888889 = 0.000000000 0.000000000 + 6.888888889x + x2 = 0 + -8.888888889 6.888888889x + x2 = 0 + -8.888888889 Combine like terms: 0 + -8.888888889 = -8.888888889 6.888888889x + x2 = -8.888888889 The x term is 6.888888889x. Take half its coefficient (3.444444445). Square it (11.86419753) and add it to both sides. Add '11.86419753' to each side of the equation. 6.888888889x + 11.86419753 + x2 = -8.888888889 + 11.86419753 Reorder the terms: 11.86419753 + 6.888888889x + x2 = -8.888888889 + 11.86419753 Combine like terms: -8.888888889 + 11.86419753 = 2.975308641 11.86419753 + 6.888888889x + x2 = 2.975308641 Factor a perfect square on the left side: (x + 3.444444445)(x + 3.444444445) = 2.975308641 Calculate the square root of the right side: 1.724908299 Break this problem into two subproblems by setting (x + 3.444444445) equal to 1.724908299 and -1.724908299.Subproblem 1
x + 3.444444445 = 1.724908299 Simplifying x + 3.444444445 = 1.724908299 Reorder the terms: 3.444444445 + x = 1.724908299 Solving 3.444444445 + x = 1.724908299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = 1.724908299 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = 1.724908299 + -3.444444445 x = 1.724908299 + -3.444444445 Combine like terms: 1.724908299 + -3.444444445 = -1.719536146 x = -1.719536146 Simplifying x = -1.719536146Subproblem 2
x + 3.444444445 = -1.724908299 Simplifying x + 3.444444445 = -1.724908299 Reorder the terms: 3.444444445 + x = -1.724908299 Solving 3.444444445 + x = -1.724908299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.444444445' to each side of the equation. 3.444444445 + -3.444444445 + x = -1.724908299 + -3.444444445 Combine like terms: 3.444444445 + -3.444444445 = 0.000000000 0.000000000 + x = -1.724908299 + -3.444444445 x = -1.724908299 + -3.444444445 Combine like terms: -1.724908299 + -3.444444445 = -5.169352744 x = -5.169352744 Simplifying x = -5.169352744Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.719536146, -5.169352744}
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