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Simplifying 8 + 5(9 + 4x) * x = 2 Reorder the terms for easier multiplication: 8 + 5x(9 + 4x) = 2 8 + (9 * 5x + 4x * 5x) = 2 8 + (45x + 20x2) = 2 Solving 8 + 45x + 20x2 = 2 Solving for variable 'x'. Reorder the terms: 8 + -2 + 45x + 20x2 = 2 + -2 Combine like terms: 8 + -2 = 6 6 + 45x + 20x2 = 2 + -2 Combine like terms: 2 + -2 = 0 6 + 45x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.3 + 2.25x + x2 = 0.0 Move the constant term to the right: Add '-0.3' to each side of the equation. 0.3 + 2.25x + -0.3 + x2 = 0.0 + -0.3 Reorder the terms: 0.3 + -0.3 + 2.25x + x2 = 0.0 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + 2.25x + x2 = 0.0 + -0.3 2.25x + x2 = 0.0 + -0.3 Combine like terms: 0.0 + -0.3 = -0.3 2.25x + x2 = -0.3 The x term is 2.25x. Take half its coefficient (1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. 2.25x + 1.265625 + x2 = -0.3 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = -0.3 + 1.265625 Combine like terms: -0.3 + 1.265625 = 0.965625 1.265625 + 2.25x + x2 = 0.965625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 0.965625 Calculate the square root of the right side: 0.9826622 Break this problem into two subproblems by setting (x + 1.125) equal to 0.9826622 and -0.9826622.Subproblem 1
x + 1.125 = 0.9826622 Simplifying x + 1.125 = 0.9826622 Reorder the terms: 1.125 + x = 0.9826622 Solving 1.125 + x = 0.9826622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.9826622 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.9826622 + -1.125 x = 0.9826622 + -1.125 Combine like terms: 0.9826622 + -1.125 = -0.1423378 x = -0.1423378 Simplifying x = -0.1423378Subproblem 2
x + 1.125 = -0.9826622 Simplifying x + 1.125 = -0.9826622 Reorder the terms: 1.125 + x = -0.9826622 Solving 1.125 + x = -0.9826622 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.9826622 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.9826622 + -1.125 x = -0.9826622 + -1.125 Combine like terms: -0.9826622 + -1.125 = -2.1076622 x = -2.1076622 Simplifying x = -2.1076622Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1423378, -2.1076622}
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