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Simplifying (5x + 1)(5x + 1) + 3 = 10 Reorder the terms: (1 + 5x)(5x + 1) + 3 = 10 Reorder the terms: (1 + 5x)(1 + 5x) + 3 = 10 Multiply (1 + 5x) * (1 + 5x) (1(1 + 5x) + 5x * (1 + 5x)) + 3 = 10 ((1 * 1 + 5x * 1) + 5x * (1 + 5x)) + 3 = 10 ((1 + 5x) + 5x * (1 + 5x)) + 3 = 10 (1 + 5x + (1 * 5x + 5x * 5x)) + 3 = 10 (1 + 5x + (5x + 25x2)) + 3 = 10 Combine like terms: 5x + 5x = 10x (1 + 10x + 25x2) + 3 = 10 Reorder the terms: 1 + 3 + 10x + 25x2 = 10 Combine like terms: 1 + 3 = 4 4 + 10x + 25x2 = 10 Solving 4 + 10x + 25x2 = 10 Solving for variable 'x'. Reorder the terms: 4 + -10 + 10x + 25x2 = 10 + -10 Combine like terms: 4 + -10 = -6 -6 + 10x + 25x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -6 + 10x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.24 + 0.4x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + 0.4x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + 0.4x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + 0.4x + x2 = 0 + 0.24 0.4x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 0.4x + x2 = 0.24 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 0.24 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 0.24 + 0.04 Combine like terms: 0.24 + 0.04 = 0.28 0.04 + 0.4x + x2 = 0.28 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 0.28 Calculate the square root of the right side: 0.529150262 Break this problem into two subproblems by setting (x + 0.2) equal to 0.529150262 and -0.529150262.Subproblem 1
x + 0.2 = 0.529150262 Simplifying x + 0.2 = 0.529150262 Reorder the terms: 0.2 + x = 0.529150262 Solving 0.2 + x = 0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 0.529150262 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 0.529150262 + -0.2 x = 0.529150262 + -0.2 Combine like terms: 0.529150262 + -0.2 = 0.329150262 x = 0.329150262 Simplifying x = 0.329150262Subproblem 2
x + 0.2 = -0.529150262 Simplifying x + 0.2 = -0.529150262 Reorder the terms: 0.2 + x = -0.529150262 Solving 0.2 + x = -0.529150262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -0.529150262 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -0.529150262 + -0.2 x = -0.529150262 + -0.2 Combine like terms: -0.529150262 + -0.2 = -0.729150262 x = -0.729150262 Simplifying x = -0.729150262Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.329150262, -0.729150262}
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