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Simplifying 0 = 9x2 + -80x + 160 Reorder the terms: 0 = 160 + -80x + 9x2 Solving 0 = 160 + -80x + 9x2 Solving for variable 'x'. Combine like terms: 0 + -160 = -160 -160 + 80x + -9x2 = 160 + -80x + 9x2 + -160 + 80x + -9x2 Reorder the terms: -160 + 80x + -9x2 = 160 + -160 + -80x + 80x + 9x2 + -9x2 Combine like terms: 160 + -160 = 0 -160 + 80x + -9x2 = 0 + -80x + 80x + 9x2 + -9x2 -160 + 80x + -9x2 = -80x + 80x + 9x2 + -9x2 Combine like terms: -80x + 80x = 0 -160 + 80x + -9x2 = 0 + 9x2 + -9x2 -160 + 80x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -160 + 80x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 17.77777778 + -8.888888889x + x2 = 0 Move the constant term to the right: Add '-17.77777778' to each side of the equation. 17.77777778 + -8.888888889x + -17.77777778 + x2 = 0 + -17.77777778 Reorder the terms: 17.77777778 + -17.77777778 + -8.888888889x + x2 = 0 + -17.77777778 Combine like terms: 17.77777778 + -17.77777778 = 0.00000000 0.00000000 + -8.888888889x + x2 = 0 + -17.77777778 -8.888888889x + x2 = 0 + -17.77777778 Combine like terms: 0 + -17.77777778 = -17.77777778 -8.888888889x + x2 = -17.77777778 The x term is -8.888888889x. Take half its coefficient (-4.444444445). Square it (19.75308642) and add it to both sides. Add '19.75308642' to each side of the equation. -8.888888889x + 19.75308642 + x2 = -17.77777778 + 19.75308642 Reorder the terms: 19.75308642 + -8.888888889x + x2 = -17.77777778 + 19.75308642 Combine like terms: -17.77777778 + 19.75308642 = 1.97530864 19.75308642 + -8.888888889x + x2 = 1.97530864 Factor a perfect square on the left side: (x + -4.444444445)(x + -4.444444445) = 1.97530864 Calculate the square root of the right side: 1.405456737 Break this problem into two subproblems by setting (x + -4.444444445) equal to 1.405456737 and -1.405456737.Subproblem 1
x + -4.444444445 = 1.405456737 Simplifying x + -4.444444445 = 1.405456737 Reorder the terms: -4.444444445 + x = 1.405456737 Solving -4.444444445 + x = 1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = 1.405456737 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = 1.405456737 + 4.444444445 x = 1.405456737 + 4.444444445 Combine like terms: 1.405456737 + 4.444444445 = 5.849901182 x = 5.849901182 Simplifying x = 5.849901182Subproblem 2
x + -4.444444445 = -1.405456737 Simplifying x + -4.444444445 = -1.405456737 Reorder the terms: -4.444444445 + x = -1.405456737 Solving -4.444444445 + x = -1.405456737 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.444444445' to each side of the equation. -4.444444445 + 4.444444445 + x = -1.405456737 + 4.444444445 Combine like terms: -4.444444445 + 4.444444445 = 0.000000000 0.000000000 + x = -1.405456737 + 4.444444445 x = -1.405456737 + 4.444444445 Combine like terms: -1.405456737 + 4.444444445 = 3.038987708 x = 3.038987708 Simplifying x = 3.038987708Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.849901182, 3.038987708}
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