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Simplifying 25x2 + 15x + -2 = 0 Reorder the terms: -2 + 15x + 25x2 = 0 Solving -2 + 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'. -0.08 + 0.6x + x2 = 0 Move the constant term to the right: Add '0.08' to each side of the equation. -0.08 + 0.6x + 0.08 + x2 = 0 + 0.08 Reorder the terms: -0.08 + 0.08 + 0.6x + x2 = 0 + 0.08 Combine like terms: -0.08 + 0.08 = 0.00 0.00 + 0.6x + x2 = 0 + 0.08 0.6x + x2 = 0 + 0.08 Combine like terms: 0 + 0.08 = 0.08 0.6x + x2 = 0.08 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 = 0.08 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 0.08 + 0.09 Combine like terms: 0.08 + 0.09 = 0.17 0.09 + 0.6x + x2 = 0.17 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 0.17 Calculate the square root of the right side: 0.412310563 Break this problem into two subproblems by setting (x + 0.3) equal to 0.412310563 and -0.412310563.Subproblem 1
x + 0.3 = 0.412310563 Simplifying x + 0.3 = 0.412310563 Reorder the terms: 0.3 + x = 0.412310563 Solving 0.3 + x = 0.412310563 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 = 0.412310563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 0.412310563 + -0.3 x = 0.412310563 + -0.3 Combine like terms: 0.412310563 + -0.3 = 0.112310563 x = 0.112310563 Simplifying x = 0.112310563Subproblem 2
x + 0.3 = -0.412310563 Simplifying x + 0.3 = -0.412310563 Reorder the terms: 0.3 + x = -0.412310563 Solving 0.3 + x = -0.412310563 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 = -0.412310563 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -0.412310563 + -0.3 x = -0.412310563 + -0.3 Combine like terms: -0.412310563 + -0.3 = -0.712310563 x = -0.712310563 Simplifying x = -0.712310563Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.112310563, -0.712310563}
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