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Simplifying 9 + -25x2 + 50x + 25 = 0 Reorder the terms: 9 + 25 + 50x + -25x2 = 0 Combine like terms: 9 + 25 = 34 34 + 50x + -25x2 = 0 Solving 34 + 50x + -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'. -1.36 + -2x + x2 = 0 Move the constant term to the right: Add '1.36' to each side of the equation. -1.36 + -2x + 1.36 + x2 = 0 + 1.36 Reorder the terms: -1.36 + 1.36 + -2x + x2 = 0 + 1.36 Combine like terms: -1.36 + 1.36 = 0.00 0.00 + -2x + x2 = 0 + 1.36 -2x + x2 = 0 + 1.36 Combine like terms: 0 + 1.36 = 1.36 -2x + x2 = 1.36 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.36 + 1 Reorder the terms: 1 + -2x + x2 = 1.36 + 1 Combine like terms: 1.36 + 1 = 2.36 1 + -2x + x2 = 2.36 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.36 Calculate the square root of the right side: 1.53622915 Break this problem into two subproblems by setting (x + -1) equal to 1.53622915 and -1.53622915.Subproblem 1
x + -1 = 1.53622915 Simplifying x + -1 = 1.53622915 Reorder the terms: -1 + x = 1.53622915 Solving -1 + x = 1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.53622915 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.53622915 + 1 x = 1.53622915 + 1 Combine like terms: 1.53622915 + 1 = 2.53622915 x = 2.53622915 Simplifying x = 2.53622915Subproblem 2
x + -1 = -1.53622915 Simplifying x + -1 = -1.53622915 Reorder the terms: -1 + x = -1.53622915 Solving -1 + x = -1.53622915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.53622915 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.53622915 + 1 x = -1.53622915 + 1 Combine like terms: -1.53622915 + 1 = -0.53622915 x = -0.53622915 Simplifying x = -0.53622915Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.53622915, -0.53622915}
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