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Simplifying 5x(x + 9) = x + -4 Reorder the terms: 5x(9 + x) = x + -4 (9 * 5x + x * 5x) = x + -4 (45x + 5x2) = x + -4 Reorder the terms: 45x + 5x2 = -4 + x Solving 45x + 5x2 = -4 + x Solving for variable 'x'. Reorder the terms: 4 + 45x + -1x + 5x2 = -4 + x + 4 + -1x Combine like terms: 45x + -1x = 44x 4 + 44x + 5x2 = -4 + x + 4 + -1x Reorder the terms: 4 + 44x + 5x2 = -4 + 4 + x + -1x Combine like terms: -4 + 4 = 0 4 + 44x + 5x2 = 0 + x + -1x 4 + 44x + 5x2 = x + -1x Combine like terms: x + -1x = 0 4 + 44x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.8 + 8.8x + x2 = 0 Move the constant term to the right: Add '-0.8' to each side of the equation. 0.8 + 8.8x + -0.8 + x2 = 0 + -0.8 Reorder the terms: 0.8 + -0.8 + 8.8x + x2 = 0 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + 8.8x + x2 = 0 + -0.8 8.8x + x2 = 0 + -0.8 Combine like terms: 0 + -0.8 = -0.8 8.8x + x2 = -0.8 The x term is 8.8x. Take half its coefficient (4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. 8.8x + 19.36 + x2 = -0.8 + 19.36 Reorder the terms: 19.36 + 8.8x + x2 = -0.8 + 19.36 Combine like terms: -0.8 + 19.36 = 18.56 19.36 + 8.8x + x2 = 18.56 Factor a perfect square on the left side: (x + 4.4)(x + 4.4) = 18.56 Calculate the square root of the right side: 4.308131846 Break this problem into two subproblems by setting (x + 4.4) equal to 4.308131846 and -4.308131846.Subproblem 1
x + 4.4 = 4.308131846 Simplifying x + 4.4 = 4.308131846 Reorder the terms: 4.4 + x = 4.308131846 Solving 4.4 + x = 4.308131846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = 4.308131846 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = 4.308131846 + -4.4 x = 4.308131846 + -4.4 Combine like terms: 4.308131846 + -4.4 = -0.091868154 x = -0.091868154 Simplifying x = -0.091868154Subproblem 2
x + 4.4 = -4.308131846 Simplifying x + 4.4 = -4.308131846 Reorder the terms: 4.4 + x = -4.308131846 Solving 4.4 + x = -4.308131846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.4' to each side of the equation. 4.4 + -4.4 + x = -4.308131846 + -4.4 Combine like terms: 4.4 + -4.4 = 0.0 0.0 + x = -4.308131846 + -4.4 x = -4.308131846 + -4.4 Combine like terms: -4.308131846 + -4.4 = -8.708131846 x = -8.708131846 Simplifying x = -8.708131846Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.091868154, -8.708131846}
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