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Simplifying 8x2 + 21x + -9 = 9 Reorder the terms: -9 + 21x + 8x2 = 9 Solving -9 + 21x + 8x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -9 + 21x + 8x2 = 9 + -9 Combine like terms: -9 + -9 = -18 -18 + 21x + 8x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -18 + 21x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.25 + 2.625x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 2.625x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 2.625x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 2.625x + x2 = 0 + 2.25 2.625x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 2.625x + x2 = 2.25 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 = 2.25 + 1.72265625 Reorder the terms: 1.72265625 + 2.625x + x2 = 2.25 + 1.72265625 Combine like terms: 2.25 + 1.72265625 = 3.97265625 1.72265625 + 2.625x + x2 = 3.97265625 Factor a perfect square on the left side: (x + 1.3125)(x + 1.3125) = 3.97265625 Calculate the square root of the right side: 1.99315234 Break this problem into two subproblems by setting (x + 1.3125) equal to 1.99315234 and -1.99315234.Subproblem 1
x + 1.3125 = 1.99315234 Simplifying x + 1.3125 = 1.99315234 Reorder the terms: 1.3125 + x = 1.99315234 Solving 1.3125 + x = 1.99315234 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 = 1.99315234 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = 1.99315234 + -1.3125 x = 1.99315234 + -1.3125 Combine like terms: 1.99315234 + -1.3125 = 0.68065234 x = 0.68065234 Simplifying x = 0.68065234Subproblem 2
x + 1.3125 = -1.99315234 Simplifying x + 1.3125 = -1.99315234 Reorder the terms: 1.3125 + x = -1.99315234 Solving 1.3125 + x = -1.99315234 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 = -1.99315234 + -1.3125 Combine like terms: 1.3125 + -1.3125 = 0.0000 0.0000 + x = -1.99315234 + -1.3125 x = -1.99315234 + -1.3125 Combine like terms: -1.99315234 + -1.3125 = -3.30565234 x = -3.30565234 Simplifying x = -3.30565234Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.68065234, -3.30565234}
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