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Simplifying 9x2 + -8x = 77 Reorder the terms: -8x + 9x2 = 77 Solving -8x + 9x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + -8x + 9x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + -8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8.555555556 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '8.555555556' to each side of the equation. -8.555555556 + -0.8888888889x + 8.555555556 + x2 = 0 + 8.555555556 Reorder the terms: -8.555555556 + 8.555555556 + -0.8888888889x + x2 = 0 + 8.555555556 Combine like terms: -8.555555556 + 8.555555556 = 0.000000000 0.000000000 + -0.8888888889x + x2 = 0 + 8.555555556 -0.8888888889x + x2 = 0 + 8.555555556 Combine like terms: 0 + 8.555555556 = 8.555555556 -0.8888888889x + x2 = 8.555555556 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 = 8.555555556 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 8.555555556 + 0.1975308642 Combine like terms: 8.555555556 + 0.1975308642 = 8.7530864202 0.1975308642 + -0.8888888889x + x2 = 8.7530864202 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 8.7530864202 Calculate the square root of the right side: 2.958561546 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 2.958561546 and -2.958561546.Subproblem 1
x + -0.4444444445 = 2.958561546 Simplifying x + -0.4444444445 = 2.958561546 Reorder the terms: -0.4444444445 + x = 2.958561546 Solving -0.4444444445 + x = 2.958561546 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 = 2.958561546 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 2.958561546 + 0.4444444445 x = 2.958561546 + 0.4444444445 Combine like terms: 2.958561546 + 0.4444444445 = 3.4030059905 x = 3.4030059905 Simplifying x = 3.4030059905Subproblem 2
x + -0.4444444445 = -2.958561546 Simplifying x + -0.4444444445 = -2.958561546 Reorder the terms: -0.4444444445 + x = -2.958561546 Solving -0.4444444445 + x = -2.958561546 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 = -2.958561546 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -2.958561546 + 0.4444444445 x = -2.958561546 + 0.4444444445 Combine like terms: -2.958561546 + 0.4444444445 = -2.5141171015 x = -2.5141171015 Simplifying x = -2.5141171015Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.4030059905, -2.5141171015}
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