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Simplifying (5x)(5x) + 6x + -2 = 0 Remove parenthesis around (5x) 5x(5x) + 6x + -2 = 0 Remove parenthesis around (5x) 5x * 5x + 6x + -2 = 0 Reorder the terms for easier multiplication: 5 * 5x * x + 6x + -2 = 0 Multiply 5 * 5 25x * x + 6x + -2 = 0 Multiply x * x 25x2 + 6x + -2 = 0 Reorder the terms: -2 + 6x + 25x2 = 0 Solving -2 + 6x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.08 + 0.24x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.24x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.24x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.24x + x2 = 0 + 0.08 0.24x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.24x + x2 = 0.08 The x term is 0.24x. Take half its coefficient (0.12). Square it (0.0144) and add it to both sides. Add '0.0144' to each side of the equation. 0.24x + 0.0144 + x2 = 0.08 + 0.0144 Reorder the terms: 0.0144 + 0.24x + x2 = 0.08 + 0.0144 Combine like terms: 0.08 + 0.0144 = 0.0944 0.0144 + 0.24x + x2 = 0.0944 Factor a perfect square on the left side: (x + 0.12)(x + 0.12) = 0.0944 Calculate the square root of the right side: 0.30724583 Break this problem into two subproblems by setting (x + 0.12) equal to 0.30724583 and -0.30724583.Subproblem 1
x + 0.12 = 0.30724583 Simplifying x + 0.12 = 0.30724583 Reorder the terms: 0.12 + x = 0.30724583 Solving 0.12 + x = 0.30724583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = 0.30724583 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = 0.30724583 + -0.12 x = 0.30724583 + -0.12 Combine like terms: 0.30724583 + -0.12 = 0.18724583 x = 0.18724583 Simplifying x = 0.18724583Subproblem 2
x + 0.12 = -0.30724583 Simplifying x + 0.12 = -0.30724583 Reorder the terms: 0.12 + x = -0.30724583 Solving 0.12 + x = -0.30724583 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.12' to each side of the equation. 0.12 + -0.12 + x = -0.30724583 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + x = -0.30724583 + -0.12 x = -0.30724583 + -0.12 Combine like terms: -0.30724583 + -0.12 = -0.42724583 x = -0.42724583 Simplifying x = -0.42724583Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.18724583, -0.42724583}
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