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Simplifying 0 = -9x2 + 8x + 3 Reorder the terms: 0 = 3 + 8x + -9x2 Solving 0 = 3 + 8x + -9x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -8x + 9x2 = 3 + 8x + -9x2 + -3 + -8x + 9x2 Reorder the terms: -3 + -8x + 9x2 = 3 + -3 + 8x + -8x + -9x2 + 9x2 Combine like terms: 3 + -3 = 0 -3 + -8x + 9x2 = 0 + 8x + -8x + -9x2 + 9x2 -3 + -8x + 9x2 = 8x + -8x + -9x2 + 9x2 Combine like terms: 8x + -8x = 0 -3 + -8x + 9x2 = 0 + -9x2 + 9x2 -3 + -8x + 9x2 = -9x2 + 9x2 Combine like terms: -9x2 + 9x2 = 0 -3 + -8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.3333333333 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + -0.8888888889x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + -0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.3333333333 -0.8888888889x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 -0.8888888889x + x2 = 0.3333333333 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 = 0.3333333333 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.3333333333 + 0.1975308642 Combine like terms: 0.3333333333 + 0.1975308642 = 0.5308641975 0.1975308642 + -0.8888888889x + x2 = 0.5308641975 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.5308641975 Calculate the square root of the right side: 0.72860428 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.72860428 and -0.72860428.Subproblem 1
x + -0.4444444445 = 0.72860428 Simplifying x + -0.4444444445 = 0.72860428 Reorder the terms: -0.4444444445 + x = 0.72860428 Solving -0.4444444445 + x = 0.72860428 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 = 0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.72860428 + 0.4444444445 x = 0.72860428 + 0.4444444445 Combine like terms: 0.72860428 + 0.4444444445 = 1.1730487245 x = 1.1730487245 Simplifying x = 1.1730487245Subproblem 2
x + -0.4444444445 = -0.72860428 Simplifying x + -0.4444444445 = -0.72860428 Reorder the terms: -0.4444444445 + x = -0.72860428 Solving -0.4444444445 + x = -0.72860428 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 = -0.72860428 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.72860428 + 0.4444444445 x = -0.72860428 + 0.4444444445 Combine like terms: -0.72860428 + 0.4444444445 = -0.2841598355 x = -0.2841598355 Simplifying x = -0.2841598355Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1730487245, -0.2841598355}
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