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Simplifying 0 = -9x2 + 8x + 5 Reorder the terms: 0 = 5 + 8x + -9x2 Solving 0 = 5 + 8x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -5 = -5 -5 + -8x + 9x2 = 5 + 8x + -9x2 + -5 + -8x + 9x2 Reorder the terms: -5 + -8x + 9x2 = 5 + -5 + 8x + -8x + -9x2 + 9x2 Combine like terms: 5 + -5 = 0 -5 + -8x + 9x2 = 0 + 8x + -8x + -9x2 + 9x2 -5 + -8x + 9x2 = 8x + -8x + -9x2 + 9x2 Combine like terms: 8x + -8x = 0 -5 + -8x + 9x2 = 0 + -9x2 + 9x2 -5 + -8x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -5 + -8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.5555555556 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.5555555556' to each side of the equation. -0.5555555556 + -0.8888888889x + 0.5555555556 + x2 = 0 + 0.5555555556 Reorder the terms: -0.5555555556 + 0.5555555556 + -0.8888888889x + x2 = 0 + 0.5555555556 Combine like terms: -0.5555555556 + 0.5555555556 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.5555555556 -0.8888888889x + x2 = 0 + 0.5555555556 Combine like terms: 0 + 0.5555555556 = 0.5555555556 -0.8888888889x + x2 = 0.5555555556 The x term is -0.8888888889x. Take half its coefficient (-0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. -0.8888888889x + 0.1975308642 + x2 = 0.5555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.5555555556 + 0.1975308642 Combine like terms: 0.5555555556 + 0.1975308642 = 0.7530864198 0.1975308642 + -0.8888888889x + x2 = 0.7530864198 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.7530864198 Calculate the square root of the right side: 0.86780552 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.86780552 and -0.86780552.Subproblem 1
x + -0.4444444445 = 0.86780552 Simplifying x + -0.4444444445 = 0.86780552 Reorder the terms: -0.4444444445 + x = 0.86780552 Solving -0.4444444445 + x = 0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = 0.86780552 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.86780552 + 0.4444444445 x = 0.86780552 + 0.4444444445 Combine like terms: 0.86780552 + 0.4444444445 = 1.3122499645 x = 1.3122499645 Simplifying x = 1.3122499645Subproblem 2
x + -0.4444444445 = -0.86780552 Simplifying x + -0.4444444445 = -0.86780552 Reorder the terms: -0.4444444445 + x = -0.86780552 Solving -0.4444444445 + x = -0.86780552 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4444444445' to each side of the equation. -0.4444444445 + 0.4444444445 + x = -0.86780552 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.86780552 + 0.4444444445 x = -0.86780552 + 0.4444444445 Combine like terms: -0.86780552 + 0.4444444445 = -0.4233610755 x = -0.4233610755 Simplifying x = -0.4233610755Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3122499645, -0.4233610755}
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