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Simplifying 25x2 + 15x + -33 = 0 Reorder the terms: -33 + 15x + 25x2 = 0 Solving -33 + 15x + 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'. -1.32 + 0.6x + x2 = 0 Move the constant term to the right: Add '1.32' to each side of the equation. -1.32 + 0.6x + 1.32 + x2 = 0 + 1.32 Reorder the terms: -1.32 + 1.32 + 0.6x + x2 = 0 + 1.32 Combine like terms: -1.32 + 1.32 = 0.00 0.00 + 0.6x + x2 = 0 + 1.32 0.6x + x2 = 0 + 1.32 Combine like terms: 0 + 1.32 = 1.32 0.6x + x2 = 1.32 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 1.32 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 1.32 + 0.09 Combine like terms: 1.32 + 0.09 = 1.41 0.09 + 0.6x + x2 = 1.41 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + 0.3) equal to 1.187434209 and -1.187434209.Subproblem 1
x + 0.3 = 1.187434209 Simplifying x + 0.3 = 1.187434209 Reorder the terms: 0.3 + x = 1.187434209 Solving 0.3 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 1.187434209 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 1.187434209 + -0.3 x = 1.187434209 + -0.3 Combine like terms: 1.187434209 + -0.3 = 0.887434209 x = 0.887434209 Simplifying x = 0.887434209Subproblem 2
x + 0.3 = -1.187434209 Simplifying x + 0.3 = -1.187434209 Reorder the terms: 0.3 + x = -1.187434209 Solving 0.3 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -1.187434209 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -1.187434209 + -0.3 x = -1.187434209 + -0.3 Combine like terms: -1.187434209 + -0.3 = -1.487434209 x = -1.487434209 Simplifying x = -1.487434209Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.887434209, -1.487434209}
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