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Simplifying 8x2 = 9 + -5x Solving 8x2 = 9 + -5x Solving for variable 'x'. Reorder the terms: -9 + 5x + 8x2 = 9 + -5x + -9 + 5x Reorder the terms: -9 + 5x + 8x2 = 9 + -9 + -5x + 5x Combine like terms: 9 + -9 = 0 -9 + 5x + 8x2 = 0 + -5x + 5x -9 + 5x + 8x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -9 + 5x + 8x2 = 0 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 = 0.793237876 x = 0.793237876 Simplifying x = 0.793237876Subproblem 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 = -1.418237876 x = -1.418237876 Simplifying x = -1.418237876Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.793237876, -1.418237876}
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