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Simplifying x2 + 25x + 3 + 3x + 15 + -3 = 0 Reorder the terms: 3 + 15 + -3 + 25x + 3x + x2 = 0 Combine like terms: 3 + 15 = 18 18 + -3 + 25x + 3x + x2 = 0 Combine like terms: 18 + -3 = 15 15 + 25x + 3x + x2 = 0 Combine like terms: 25x + 3x = 28x 15 + 28x + x2 = 0 Solving 15 + 28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 28x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 28x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 28x + x2 = 0 + -15 28x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 28x + x2 = -15 The x term is 28x. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28x + 196 + x2 = -15 + 196 Reorder the terms: 196 + 28x + x2 = -15 + 196 Combine like terms: -15 + 196 = 181 196 + 28x + x2 = 181 Factor a perfect square on the left side: (x + 14)(x + 14) = 181 Calculate the square root of the right side: 13.453624047 Break this problem into two subproblems by setting (x + 14) equal to 13.453624047 and -13.453624047.Subproblem 1
x + 14 = 13.453624047 Simplifying x + 14 = 13.453624047 Reorder the terms: 14 + x = 13.453624047 Solving 14 + x = 13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 13.453624047 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.453624047 + -14 x = 13.453624047 + -14 Combine like terms: 13.453624047 + -14 = -0.546375953 x = -0.546375953 Simplifying x = -0.546375953Subproblem 2
x + 14 = -13.453624047 Simplifying x + 14 = -13.453624047 Reorder the terms: 14 + x = -13.453624047 Solving 14 + x = -13.453624047 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -13.453624047 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.453624047 + -14 x = -13.453624047 + -14 Combine like terms: -13.453624047 + -14 = -27.453624047 x = -27.453624047 Simplifying x = -27.453624047Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.546375953, -27.453624047}
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