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Simplifying 1.25x2 + 35x + -25 = 0 Reorder the terms: -25 + 35x + 1.25x2 = 0 Solving -25 + 35x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -20 + 28x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 28x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 28x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 28x + x2 = 0 + 20 28x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 28x + x2 = 20 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 = 20 + 196 Reorder the terms: 196 + 28x + x2 = 20 + 196 Combine like terms: 20 + 196 = 216 196 + 28x + x2 = 216 Factor a perfect square on the left side: (x + 14)(x + 14) = 216 Calculate the square root of the right side: 14.696938457 Break this problem into two subproblems by setting (x + 14) equal to 14.696938457 and -14.696938457.Subproblem 1
x + 14 = 14.696938457 Simplifying x + 14 = 14.696938457 Reorder the terms: 14 + x = 14.696938457 Solving 14 + x = 14.696938457 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 = 14.696938457 + -14 Combine like terms: 14 + -14 = 0 0 + x = 14.696938457 + -14 x = 14.696938457 + -14 Combine like terms: 14.696938457 + -14 = 0.696938457 x = 0.696938457 Simplifying x = 0.696938457Subproblem 2
x + 14 = -14.696938457 Simplifying x + 14 = -14.696938457 Reorder the terms: 14 + x = -14.696938457 Solving 14 + x = -14.696938457 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 = -14.696938457 + -14 Combine like terms: 14 + -14 = 0 0 + x = -14.696938457 + -14 x = -14.696938457 + -14 Combine like terms: -14.696938457 + -14 = -28.696938457 x = -28.696938457 Simplifying x = -28.696938457Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.696938457, -28.696938457}
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