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Simplifying 8x2 + 21x + -45 = 0 Reorder the terms: -45 + 21x + 8x2 = 0 Solving -45 + 21x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + 2.625x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + 2.625x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + 2.625x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + 2.625x + x2 = 0 + 5.625 2.625x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 2.625x + x2 = 5.625 The x term is 2.625x. Take half its coefficient (1.3125). Square it (1.72265625) and add it to both sides. Add '1.72265625' to each side of the equation. 2.625x + 1.72265625 + x2 = 5.625 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = 5.625 + 1.72265625 Combine like terms: 5.625 + 1.72265625 = 7.34765625 1.72265625 + 2.625x + x2 = 7.34765625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 7.34765625 Calculate the square root of the right side: 2.710656055 Break this problem into two subproblems by setting (x + 1.3125) equal to 2.710656055 and -2.710656055.Subproblem 1
x + 1.3125 = 2.710656055 Simplifying x + 1.3125 = 2.710656055 Reorder the terms: 1.3125 + x = 2.710656055 Solving 1.3125 + x = 2.710656055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = 2.710656055 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 2.710656055 + -1.3125 x = 2.710656055 + -1.3125 Combine like terms: 2.710656055 + -1.3125 = 1.398156055 x = 1.398156055 Simplifying x = 1.398156055Subproblem 2
x + 1.3125 = -2.710656055 Simplifying x + 1.3125 = -2.710656055 Reorder the terms: 1.3125 + x = -2.710656055 Solving 1.3125 + x = -2.710656055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.3125' to each side of the equation. 1.3125 + -1.3125 + x = -2.710656055 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -2.710656055 + -1.3125 x = -2.710656055 + -1.3125 Combine like terms: -2.710656055 + -1.3125 = -4.023156055 x = -4.023156055 Simplifying x = -4.023156055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.398156055, -4.023156055}
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