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Simplifying 5x(x + 2) = 8 + 4(5 + -1x) Reorder the terms: 5x(2 + x) = 8 + 4(5 + -1x) (2 * 5x + x * 5x) = 8 + 4(5 + -1x) (10x + 5x2) = 8 + 4(5 + -1x) 10x + 5x2 = 8 + (5 * 4 + -1x * 4) 10x + 5x2 = 8 + (20 + -4x) Combine like terms: 8 + 20 = 28 10x + 5x2 = 28 + -4x Solving 10x + 5x2 = 28 + -4x Solving for variable 'x'. Reorder the terms: -28 + 10x + 4x + 5x2 = 28 + -4x + -28 + 4x Combine like terms: 10x + 4x = 14x -28 + 14x + 5x2 = 28 + -4x + -28 + 4x Reorder the terms: -28 + 14x + 5x2 = 28 + -28 + -4x + 4x Combine like terms: 28 + -28 = 0 -28 + 14x + 5x2 = 0 + -4x + 4x -28 + 14x + 5x2 = -4x + 4x Combine like terms: -4x + 4x = 0 -28 + 14x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.6 + 2.8x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + 2.8x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + 2.8x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + 2.8x + x2 = 0 + 5.6 2.8x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 2.8x + x2 = 5.6 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 5.6 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 5.6 + 1.96 Combine like terms: 5.6 + 1.96 = 7.56 1.96 + 2.8x + x2 = 7.56 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 7.56 Calculate the square root of the right side: 2.749545417 Break this problem into two subproblems by setting (x + 1.4) equal to 2.749545417 and -2.749545417.Subproblem 1
x + 1.4 = 2.749545417 Simplifying x + 1.4 = 2.749545417 Reorder the terms: 1.4 + x = 2.749545417 Solving 1.4 + x = 2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 2.749545417 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 2.749545417 + -1.4 x = 2.749545417 + -1.4 Combine like terms: 2.749545417 + -1.4 = 1.349545417 x = 1.349545417 Simplifying x = 1.349545417Subproblem 2
x + 1.4 = -2.749545417 Simplifying x + 1.4 = -2.749545417 Reorder the terms: 1.4 + x = -2.749545417 Solving 1.4 + x = -2.749545417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -2.749545417 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -2.749545417 + -1.4 x = -2.749545417 + -1.4 Combine like terms: -2.749545417 + -1.4 = -4.149545417 x = -4.149545417 Simplifying x = -4.149545417Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.349545417, -4.149545417}
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