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Simplifying x = 5x(x + 8) + 5(2x + -1) Reorder the terms: x = 5x(8 + x) + 5(2x + -1) x = (8 * 5x + x * 5x) + 5(2x + -1) x = (40x + 5x2) + 5(2x + -1) Reorder the terms: x = 40x + 5x2 + 5(-1 + 2x) x = 40x + 5x2 + (-1 * 5 + 2x * 5) x = 40x + 5x2 + (-5 + 10x) Reorder the terms: x = -5 + 40x + 10x + 5x2 Combine like terms: 40x + 10x = 50x x = -5 + 50x + 5x2 Solving x = -5 + 50x + 5x2 Solving for variable 'x'. Reorder the terms: 5 + x + -50x + -5x2 = -5 + 50x + 5x2 + 5 + -50x + -5x2 Combine like terms: x + -50x = -49x 5 + -49x + -5x2 = -5 + 50x + 5x2 + 5 + -50x + -5x2 Reorder the terms: 5 + -49x + -5x2 = -5 + 5 + 50x + -50x + 5x2 + -5x2 Combine like terms: -5 + 5 = 0 5 + -49x + -5x2 = 0 + 50x + -50x + 5x2 + -5x2 5 + -49x + -5x2 = 50x + -50x + 5x2 + -5x2 Combine like terms: 50x + -50x = 0 5 + -49x + -5x2 = 0 + 5x2 + -5x2 5 + -49x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 5 + -49x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1 + 9.8x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 9.8x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 9.8x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 9.8x + x2 = 0 + 1 9.8x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 9.8x + x2 = 1 The x term is 9.8x. Take half its coefficient (4.9). Square it (24.01) and add it to both sides. Add '24.01' to each side of the equation. 9.8x + 24.01 + x2 = 1 + 24.01 Reorder the terms: 24.01 + 9.8x + x2 = 1 + 24.01 Combine like terms: 1 + 24.01 = 25.01 24.01 + 9.8x + x2 = 25.01 Factor a perfect square on the left side: (x + 4.9)(x + 4.9) = 25.01 Calculate the square root of the right side: 5.0009999 Break this problem into two subproblems by setting (x + 4.9) equal to 5.0009999 and -5.0009999.Subproblem 1
x + 4.9 = 5.0009999 Simplifying x + 4.9 = 5.0009999 Reorder the terms: 4.9 + x = 5.0009999 Solving 4.9 + x = 5.0009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = 5.0009999 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = 5.0009999 + -4.9 x = 5.0009999 + -4.9 Combine like terms: 5.0009999 + -4.9 = 0.1009999 x = 0.1009999 Simplifying x = 0.1009999Subproblem 2
x + 4.9 = -5.0009999 Simplifying x + 4.9 = -5.0009999 Reorder the terms: 4.9 + x = -5.0009999 Solving 4.9 + x = -5.0009999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9' to each side of the equation. 4.9 + -4.9 + x = -5.0009999 + -4.9 Combine like terms: 4.9 + -4.9 = 0.0 0.0 + x = -5.0009999 + -4.9 x = -5.0009999 + -4.9 Combine like terms: -5.0009999 + -4.9 = -9.9009999 x = -9.9009999 Simplifying x = -9.9009999Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1009999, -9.9009999}
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