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Simplifying 25x2 + 30x + -8 = 0 Reorder the terms: -8 + 30x + 25x2 = 0 Solving -8 + 30x + 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'. -0.32 + 1.2x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + 1.2x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + 1.2x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + 1.2x + x2 = 0 + 0.32 1.2x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 1.2x + x2 = 0.32 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 = 0.32 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 0.32 + 0.36 Combine like terms: 0.32 + 0.36 = 0.68 0.36 + 1.2x + x2 = 0.68 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 0.68 Calculate the square root of the right side: 0.824621125 Break this problem into two subproblems by setting (x + 0.6) equal to 0.824621125 and -0.824621125.Subproblem 1
x + 0.6 = 0.824621125 Simplifying x + 0.6 = 0.824621125 Reorder the terms: 0.6 + x = 0.824621125 Solving 0.6 + x = 0.824621125 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 = 0.824621125 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 0.824621125 + -0.6 x = 0.824621125 + -0.6 Combine like terms: 0.824621125 + -0.6 = 0.224621125 x = 0.224621125 Simplifying x = 0.224621125Subproblem 2
x + 0.6 = -0.824621125 Simplifying x + 0.6 = -0.824621125 Reorder the terms: 0.6 + x = -0.824621125 Solving 0.6 + x = -0.824621125 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 = -0.824621125 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -0.824621125 + -0.6 x = -0.824621125 + -0.6 Combine like terms: -0.824621125 + -0.6 = -1.424621125 x = -1.424621125 Simplifying x = -1.424621125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.224621125, -1.424621125}
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