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Simplifying 8x2 + -5x + -9 = 0 Reorder the terms: -9 + -5x + 8x2 = 0 Solving -9 + -5x + 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'. -1.125 + -0.625x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.625x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.625x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.625x + x2 = 0 + 1.125 -0.625x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.625x + x2 = 1.125 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 1.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 1.125 + 0.09765625 Combine like terms: 1.125 + 0.09765625 = 1.22265625 0.09765625 + -0.625x + x2 = 1.22265625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (x + -0.3125) equal to 1.105737876 and -1.105737876.Subproblem 1
x + -0.3125 = 1.105737876 Simplifying x + -0.3125 = 1.105737876 Reorder the terms: -0.3125 + x = 1.105737876 Solving -0.3125 + x = 1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 1.105737876 + 0.3125 x = 1.105737876 + 0.3125 Combine like terms: 1.105737876 + 0.3125 = 1.418237876 x = 1.418237876 Simplifying x = 1.418237876Subproblem 2
x + -0.3125 = -1.105737876 Simplifying x + -0.3125 = -1.105737876 Reorder the terms: -0.3125 + x = -1.105737876 Solving -0.3125 + x = -1.105737876 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -1.105737876 + 0.3125 x = -1.105737876 + 0.3125 Combine like terms: -1.105737876 + 0.3125 = -0.793237876 x = -0.793237876 Simplifying x = -0.793237876Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.418237876, -0.793237876}
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