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Simplifying 9x2 + 8x + -2 = 33 Reorder the terms: -2 + 8x + 9x2 = 33 Solving -2 + 8x + 9x2 = 33 Solving for variable 'x'. Reorder the terms: -2 + -33 + 8x + 9x2 = 33 + -33 Combine like terms: -2 + -33 = -35 -35 + 8x + 9x2 = 33 + -33 Combine like terms: 33 + -33 = 0 -35 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.888888889 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + 0.8888888889x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + 0.8888888889x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + 0.8888888889x + x2 = 0 + 3.888888889 0.8888888889x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 0.8888888889x + x2 = 3.888888889 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 = 3.888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 3.888888889 + 0.1975308642 Combine like terms: 3.888888889 + 0.1975308642 = 4.0864197532 0.1975308642 + 0.8888888889x + x2 = 4.0864197532 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 4.0864197532 Calculate the square root of the right side: 2.021489489 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 2.021489489 and -2.021489489.Subproblem 1
x + 0.4444444445 = 2.021489489 Simplifying x + 0.4444444445 = 2.021489489 Reorder the terms: 0.4444444445 + x = 2.021489489 Solving 0.4444444445 + x = 2.021489489 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 = 2.021489489 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 2.021489489 + -0.4444444445 x = 2.021489489 + -0.4444444445 Combine like terms: 2.021489489 + -0.4444444445 = 1.5770450445 x = 1.5770450445 Simplifying x = 1.5770450445Subproblem 2
x + 0.4444444445 = -2.021489489 Simplifying x + 0.4444444445 = -2.021489489 Reorder the terms: 0.4444444445 + x = -2.021489489 Solving 0.4444444445 + x = -2.021489489 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 = -2.021489489 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -2.021489489 + -0.4444444445 x = -2.021489489 + -0.4444444445 Combine like terms: -2.021489489 + -0.4444444445 = -2.4659339335 x = -2.4659339335 Simplifying x = -2.4659339335Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5770450445, -2.4659339335}
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