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Simplifying 5x(x + 1) = 4(x + 8) Reorder the terms: 5x(1 + x) = 4(x + 8) (1 * 5x + x * 5x) = 4(x + 8) (5x + 5x2) = 4(x + 8) Reorder the terms: 5x + 5x2 = 4(8 + x) 5x + 5x2 = (8 * 4 + x * 4) 5x + 5x2 = (32 + 4x) Solving 5x + 5x2 = 32 + 4x Solving for variable 'x'. Reorder the terms: -32 + 5x + -4x + 5x2 = 32 + 4x + -32 + -4x Combine like terms: 5x + -4x = 1x -32 + 1x + 5x2 = 32 + 4x + -32 + -4x Reorder the terms: -32 + 1x + 5x2 = 32 + -32 + 4x + -4x Combine like terms: 32 + -32 = 0 -32 + 1x + 5x2 = 0 + 4x + -4x -32 + 1x + 5x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -32 + 1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6.4 + 0.2x + x2 = 0 Move the constant term to the right: Add '6.4' to each side of the equation. -6.4 + 0.2x + 6.4 + x2 = 0 + 6.4 Reorder the terms: -6.4 + 6.4 + 0.2x + x2 = 0 + 6.4 Combine like terms: -6.4 + 6.4 = 0.0 0.0 + 0.2x + x2 = 0 + 6.4 0.2x + x2 = 0 + 6.4 Combine like terms: 0 + 6.4 = 6.4 0.2x + x2 = 6.4 The x term is 0.2x. Take half its coefficient (0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. 0.2x + 0.01 + x2 = 6.4 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 6.4 + 0.01 Combine like terms: 6.4 + 0.01 = 6.41 0.01 + 0.2x + x2 = 6.41 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 6.41 Calculate the square root of the right side: 2.53179778 Break this problem into two subproblems by setting (x + 0.1) equal to 2.53179778 and -2.53179778.Subproblem 1
x + 0.1 = 2.53179778 Simplifying x + 0.1 = 2.53179778 Reorder the terms: 0.1 + x = 2.53179778 Solving 0.1 + x = 2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = 2.53179778 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 2.53179778 + -0.1 x = 2.53179778 + -0.1 Combine like terms: 2.53179778 + -0.1 = 2.43179778 x = 2.43179778 Simplifying x = 2.43179778Subproblem 2
x + 0.1 = -2.53179778 Simplifying x + 0.1 = -2.53179778 Reorder the terms: 0.1 + x = -2.53179778 Solving 0.1 + x = -2.53179778 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1' to each side of the equation. 0.1 + -0.1 + x = -2.53179778 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -2.53179778 + -0.1 x = -2.53179778 + -0.1 Combine like terms: -2.53179778 + -0.1 = -2.63179778 x = -2.63179778 Simplifying x = -2.63179778Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.43179778, -2.63179778}
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