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Simplifying 0 = 3.25x2 + -9.75x + -25.43 Reorder the terms: 0 = -25.43 + -9.75x + 3.25x2 Solving 0 = -25.43 + -9.75x + 3.25x2 Solving for variable 'x'. Combine like terms: 0 + 25.43 = 25.43 25.43 + 9.75x + -3.25x2 = -25.43 + -9.75x + 3.25x2 + 25.43 + 9.75x + -3.25x2 Reorder the terms: 25.43 + 9.75x + -3.25x2 = -25.43 + 25.43 + -9.75x + 9.75x + 3.25x2 + -3.25x2 Combine like terms: -25.43 + 25.43 = 0.00 25.43 + 9.75x + -3.25x2 = 0.00 + -9.75x + 9.75x + 3.25x2 + -3.25x2 25.43 + 9.75x + -3.25x2 = -9.75x + 9.75x + 3.25x2 + -3.25x2 Combine like terms: -9.75x + 9.75x = 0.00 25.43 + 9.75x + -3.25x2 = 0.00 + 3.25x2 + -3.25x2 25.43 + 9.75x + -3.25x2 = 3.25x2 + -3.25x2 Combine like terms: 3.25x2 + -3.25x2 = 0.00 25.43 + 9.75x + -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'. -7.824615385 + -3x + x2 = 0 Move the constant term to the right: Add '7.824615385' to each side of the equation. -7.824615385 + -3x + 7.824615385 + x2 = 0 + 7.824615385 Reorder the terms: -7.824615385 + 7.824615385 + -3x + x2 = 0 + 7.824615385 Combine like terms: -7.824615385 + 7.824615385 = 0.000000000 0.000000000 + -3x + x2 = 0 + 7.824615385 -3x + x2 = 0 + 7.824615385 Combine like terms: 0 + 7.824615385 = 7.824615385 -3x + x2 = 7.824615385 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 7.824615385 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 7.824615385 + 2.25 Combine like terms: 7.824615385 + 2.25 = 10.074615385 2.25 + -3x + x2 = 10.074615385 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.074615385 Calculate the square root of the right side: 3.174053463 Break this problem into two subproblems by setting (x + -1.5) equal to 3.174053463 and -3.174053463.Subproblem 1
x + -1.5 = 3.174053463 Simplifying x + -1.5 = 3.174053463 Reorder the terms: -1.5 + x = 3.174053463 Solving -1.5 + x = 3.174053463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.174053463 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.174053463 + 1.5 x = 3.174053463 + 1.5 Combine like terms: 3.174053463 + 1.5 = 4.674053463 x = 4.674053463 Simplifying x = 4.674053463Subproblem 2
x + -1.5 = -3.174053463 Simplifying x + -1.5 = -3.174053463 Reorder the terms: -1.5 + x = -3.174053463 Solving -1.5 + x = -3.174053463 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.174053463 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.174053463 + 1.5 x = -3.174053463 + 1.5 Combine like terms: -3.174053463 + 1.5 = -1.674053463 x = -1.674053463 Simplifying x = -1.674053463Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.674053463, -1.674053463}
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