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Simplifying (5x + 3)(5x + 3) = 3 Reorder the terms: (3 + 5x)(5x + 3) = 3 Reorder the terms: (3 + 5x)(3 + 5x) = 3 Multiply (3 + 5x) * (3 + 5x) (3(3 + 5x) + 5x * (3 + 5x)) = 3 ((3 * 3 + 5x * 3) + 5x * (3 + 5x)) = 3 ((9 + 15x) + 5x * (3 + 5x)) = 3 (9 + 15x + (3 * 5x + 5x * 5x)) = 3 (9 + 15x + (15x + 25x2)) = 3 Combine like terms: 15x + 15x = 30x (9 + 30x + 25x2) = 3 Solving 9 + 30x + 25x2 = 3 Solving for variable 'x'. Reorder the terms: 9 + -3 + 30x + 25x2 = 3 + -3 Combine like terms: 9 + -3 = 6 6 + 30x + 25x2 = 3 + -3 Combine like terms: 3 + -3 = 0 6 + 30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.24 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.24' to each side of the equation. 0.24 + 1.2x + -0.24 + x2 = 0 + -0.24 Reorder the terms: 0.24 + -0.24 + 1.2x + x2 = 0 + -0.24 Combine like terms: 0.24 + -0.24 = 0.00 0.00 + 1.2x + x2 = 0 + -0.24 1.2x + x2 = 0 + -0.24 Combine like terms: 0 + -0.24 = -0.24 1.2x + x2 = -0.24 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = -0.24 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.24 + 0.36 Combine like terms: -0.24 + 0.36 = 0.12 0.36 + 1.2x + x2 = 0.12 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.12 Calculate the square root of the right side: 0.346410162 Break this problem into two subproblems by setting (x + 0.6) equal to 0.346410162 and -0.346410162.Subproblem 1
x + 0.6 = 0.346410162 Simplifying x + 0.6 = 0.346410162 Reorder the terms: 0.6 + x = 0.346410162 Solving 0.6 + x = 0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 0.346410162 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.346410162 + -0.6 x = 0.346410162 + -0.6 Combine like terms: 0.346410162 + -0.6 = -0.253589838 x = -0.253589838 Simplifying x = -0.253589838Subproblem 2
x + 0.6 = -0.346410162 Simplifying x + 0.6 = -0.346410162 Reorder the terms: 0.6 + x = -0.346410162 Solving 0.6 + x = -0.346410162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -0.346410162 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.346410162 + -0.6 x = -0.346410162 + -0.6 Combine like terms: -0.346410162 + -0.6 = -0.946410162 x = -0.946410162 Simplifying x = -0.946410162Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.253589838, -0.946410162}
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