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Simplifying 0 = 3.25x2 + -2.25x + -25.437 Reorder the terms: 0 = -25.437 + -2.25x + 3.25x2 Solving 0 = -25.437 + -2.25x + 3.25x2 Solving for variable 'x'. Combine like terms: 0 + 25.437 = 25.437 25.437 + 2.25x + -3.25x2 = -25.437 + -2.25x + 3.25x2 + 25.437 + 2.25x + -3.25x2 Reorder the terms: 25.437 + 2.25x + -3.25x2 = -25.437 + 25.437 + -2.25x + 2.25x + 3.25x2 + -3.25x2 Combine like terms: -25.437 + 25.437 = 0.000 25.437 + 2.25x + -3.25x2 = 0.000 + -2.25x + 2.25x + 3.25x2 + -3.25x2 25.437 + 2.25x + -3.25x2 = -2.25x + 2.25x + 3.25x2 + -3.25x2 Combine like terms: -2.25x + 2.25x = 0.00 25.437 + 2.25x + -3.25x2 = 0.00 + 3.25x2 + -3.25x2 25.437 + 2.25x + -3.25x2 = 3.25x2 + -3.25x2 Combine like terms: 3.25x2 + -3.25x2 = 0.00 25.437 + 2.25x + -3.25x2 = 0.00 Begin completing the square. Divide all terms by -3.25 the coefficient of the squared term: Divide each side by '-3.25'. -7.826769231 + -0.6923076923x + x2 = 0 Move the constant term to the right: Add '7.826769231' to each side of the equation. -7.826769231 + -0.6923076923x + 7.826769231 + x2 = 0 + 7.826769231 Reorder the terms: -7.826769231 + 7.826769231 + -0.6923076923x + x2 = 0 + 7.826769231 Combine like terms: -7.826769231 + 7.826769231 = 0.000000000 0.000000000 + -0.6923076923x + x2 = 0 + 7.826769231 -0.6923076923x + x2 = 0 + 7.826769231 Combine like terms: 0 + 7.826769231 = 7.826769231 -0.6923076923x + x2 = 7.826769231 The x term is -0.6923076923x. Take half its coefficient (-0.3461538462). Square it (0.1198224852) and add it to both sides. Add '0.1198224852' to each side of the equation. -0.6923076923x + 0.1198224852 + x2 = 7.826769231 + 0.1198224852 Reorder the terms: 0.1198224852 + -0.6923076923x + x2 = 7.826769231 + 0.1198224852 Combine like terms: 7.826769231 + 0.1198224852 = 7.9465917162 0.1198224852 + -0.6923076923x + x2 = 7.9465917162 Factor a perfect square on the left side: (x + -0.3461538462)(x + -0.3461538462) = 7.9465917162 Calculate the square root of the right side: 2.818969974 Break this problem into two subproblems by setting (x + -0.3461538462) equal to 2.818969974 and -2.818969974.Subproblem 1
x + -0.3461538462 = 2.818969974 Simplifying x + -0.3461538462 = 2.818969974 Reorder the terms: -0.3461538462 + x = 2.818969974 Solving -0.3461538462 + x = 2.818969974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3461538462' to each side of the equation. -0.3461538462 + 0.3461538462 + x = 2.818969974 + 0.3461538462 Combine like terms: -0.3461538462 + 0.3461538462 = 0.0000000000 0.0000000000 + x = 2.818969974 + 0.3461538462 x = 2.818969974 + 0.3461538462 Combine like terms: 2.818969974 + 0.3461538462 = 3.1651238202 x = 3.1651238202 Simplifying x = 3.1651238202Subproblem 2
x + -0.3461538462 = -2.818969974 Simplifying x + -0.3461538462 = -2.818969974 Reorder the terms: -0.3461538462 + x = -2.818969974 Solving -0.3461538462 + x = -2.818969974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3461538462' to each side of the equation. -0.3461538462 + 0.3461538462 + x = -2.818969974 + 0.3461538462 Combine like terms: -0.3461538462 + 0.3461538462 = 0.0000000000 0.0000000000 + x = -2.818969974 + 0.3461538462 x = -2.818969974 + 0.3461538462 Combine like terms: -2.818969974 + 0.3461538462 = -2.4728161278 x = -2.4728161278 Simplifying x = -2.4728161278Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.1651238202, -2.4728161278}
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