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Simplifying 5x(x + 1) = x + 3 Reorder the terms: 5x(1 + x) = x + 3 (1 * 5x + x * 5x) = x + 3 (5x + 5x2) = x + 3 Reorder the terms: 5x + 5x2 = 3 + x Solving 5x + 5x2 = 3 + x Solving for variable 'x'. Reorder the terms: -3 + 5x + -1x + 5x2 = 3 + x + -3 + -1x Combine like terms: 5x + -1x = 4x -3 + 4x + 5x2 = 3 + x + -3 + -1x Reorder the terms: -3 + 4x + 5x2 = 3 + -3 + x + -1x Combine like terms: 3 + -3 = 0 -3 + 4x + 5x2 = 0 + x + -1x -3 + 4x + 5x2 = x + -1x Combine like terms: x + -1x = 0 -3 + 4x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.6 + 0.8x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 0.8x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 0.8x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 0.8x + x2 = 0 + 0.6 0.8x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 0.8x + x2 = 0.6 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 0.6 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 0.6 + 0.16 Combine like terms: 0.6 + 0.16 = 0.76 0.16 + 0.8x + x2 = 0.76 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 0.76 Calculate the square root of the right side: 0.871779789 Break this problem into two subproblems by setting (x + 0.4) equal to 0.871779789 and -0.871779789.Subproblem 1
x + 0.4 = 0.871779789 Simplifying x + 0.4 = 0.871779789 Reorder the terms: 0.4 + x = 0.871779789 Solving 0.4 + x = 0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 0.871779789 + -0.4 x = 0.871779789 + -0.4 Combine like terms: 0.871779789 + -0.4 = 0.471779789 x = 0.471779789 Simplifying x = 0.471779789Subproblem 2
x + 0.4 = -0.871779789 Simplifying x + 0.4 = -0.871779789 Reorder the terms: 0.4 + x = -0.871779789 Solving 0.4 + x = -0.871779789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -0.871779789 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -0.871779789 + -0.4 x = -0.871779789 + -0.4 Combine like terms: -0.871779789 + -0.4 = -1.271779789 x = -1.271779789 Simplifying x = -1.271779789Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.471779789, -1.271779789}
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