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Simplifying 9x2 + -19x + 7 = 0 Reorder the terms: 7 + -19x + 9x2 = 0 Solving 7 + -19x + 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'. 0.7777777778 + -2.111111111x + x2 = 0 Move the constant term to the right: Add '-0.7777777778' to each side of the equation. 0.7777777778 + -2.111111111x + -0.7777777778 + x2 = 0 + -0.7777777778 Reorder the terms: 0.7777777778 + -0.7777777778 + -2.111111111x + x2 = 0 + -0.7777777778 Combine like terms: 0.7777777778 + -0.7777777778 = 0.0000000000 0.0000000000 + -2.111111111x + x2 = 0 + -0.7777777778 -2.111111111x + x2 = 0 + -0.7777777778 Combine like terms: 0 + -0.7777777778 = -0.7777777778 -2.111111111x + x2 = -0.7777777778 The x term is -2.111111111x. Take half its coefficient (-1.055555556). Square it (1.114197532) and add it to both sides. Add '1.114197532' to each side of the equation. -2.111111111x + 1.114197532 + x2 = -0.7777777778 + 1.114197532 Reorder the terms: 1.114197532 + -2.111111111x + x2 = -0.7777777778 + 1.114197532 Combine like terms: -0.7777777778 + 1.114197532 = 0.3364197542 1.114197532 + -2.111111111x + x2 = 0.3364197542 Factor a perfect square on the left side: (x + -1.055555556)(x + -1.055555556) = 0.3364197542 Calculate the square root of the right side: 0.580017029 Break this problem into two subproblems by setting (x + -1.055555556) equal to 0.580017029 and -0.580017029.Subproblem 1
x + -1.055555556 = 0.580017029 Simplifying x + -1.055555556 = 0.580017029 Reorder the terms: -1.055555556 + x = 0.580017029 Solving -1.055555556 + x = 0.580017029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + x = 0.580017029 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = 0.580017029 + 1.055555556 x = 0.580017029 + 1.055555556 Combine like terms: 0.580017029 + 1.055555556 = 1.635572585 x = 1.635572585 Simplifying x = 1.635572585Subproblem 2
x + -1.055555556 = -0.580017029 Simplifying x + -1.055555556 = -0.580017029 Reorder the terms: -1.055555556 + x = -0.580017029 Solving -1.055555556 + x = -0.580017029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.055555556' to each side of the equation. -1.055555556 + 1.055555556 + x = -0.580017029 + 1.055555556 Combine like terms: -1.055555556 + 1.055555556 = 0.000000000 0.000000000 + x = -0.580017029 + 1.055555556 x = -0.580017029 + 1.055555556 Combine like terms: -0.580017029 + 1.055555556 = 0.475538527 x = 0.475538527 Simplifying x = 0.475538527Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.635572585, 0.475538527}
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