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Simplifying (5x + 3)(5x + 3) = 6 Reorder the terms: (3 + 5x)(5x + 3) = 6 Reorder the terms: (3 + 5x)(3 + 5x) = 6 Multiply (3 + 5x) * (3 + 5x) (3(3 + 5x) + 5x * (3 + 5x)) = 6 ((3 * 3 + 5x * 3) + 5x * (3 + 5x)) = 6 ((9 + 15x) + 5x * (3 + 5x)) = 6 (9 + 15x + (3 * 5x + 5x * 5x)) = 6 (9 + 15x + (15x + 25x2)) = 6 Combine like terms: 15x + 15x = 30x (9 + 30x + 25x2) = 6 Solving 9 + 30x + 25x2 = 6 Solving for variable 'x'. Reorder the terms: 9 + -6 + 30x + 25x2 = 6 + -6 Combine like terms: 9 + -6 = 3 3 + 30x + 25x2 = 6 + -6 Combine like terms: 6 + -6 = 0 3 + 30x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + 1.2x + x2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + 1.2x + -0.12 + x2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + 1.2x + x2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + 1.2x + x2 = 0 + -0.12 1.2x + x2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 1.2x + x2 = -0.12 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 = -0.12 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = -0.12 + 0.36 Combine like terms: -0.12 + 0.36 = 0.24 0.36 + 1.2x + x2 = 0.24 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.24 Calculate the square root of the right side: 0.489897949 Break this problem into two subproblems by setting (x + 0.6) equal to 0.489897949 and -0.489897949.Subproblem 1
x + 0.6 = 0.489897949 Simplifying x + 0.6 = 0.489897949 Reorder the terms: 0.6 + x = 0.489897949 Solving 0.6 + x = 0.489897949 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 = 0.489897949 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.489897949 + -0.6 x = 0.489897949 + -0.6 Combine like terms: 0.489897949 + -0.6 = -0.110102051 x = -0.110102051 Simplifying x = -0.110102051Subproblem 2
x + 0.6 = -0.489897949 Simplifying x + 0.6 = -0.489897949 Reorder the terms: 0.6 + x = -0.489897949 Solving 0.6 + x = -0.489897949 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 = -0.489897949 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.489897949 + -0.6 x = -0.489897949 + -0.6 Combine like terms: -0.489897949 + -0.6 = -1.089897949 x = -1.089897949 Simplifying x = -1.089897949Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.110102051, -1.089897949}
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