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Simplifying 5x2 + 12x + -41 = 9 Reorder the terms: -41 + 12x + 5x2 = 9 Solving -41 + 12x + 5x2 = 9 Solving for variable 'x'. Reorder the terms: -41 + -9 + 12x + 5x2 = 9 + -9 Combine like terms: -41 + -9 = -50 -50 + 12x + 5x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -50 + 12x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -10 + 2.4x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 2.4x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2.4x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2.4x + x2 = 0 + 10 2.4x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2.4x + x2 = 10 The x term is 2.4x. Take half its coefficient (1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. 2.4x + 1.44 + x2 = 10 + 1.44 Reorder the terms: 1.44 + 2.4x + x2 = 10 + 1.44 Combine like terms: 10 + 1.44 = 11.44 1.44 + 2.4x + x2 = 11.44 Factor a perfect square on the left side: (x + 1.2)(x + 1.2) = 11.44 Calculate the square root of the right side: 3.382306905 Break this problem into two subproblems by setting (x + 1.2) equal to 3.382306905 and -3.382306905.Subproblem 1
x + 1.2 = 3.382306905 Simplifying x + 1.2 = 3.382306905 Reorder the terms: 1.2 + x = 3.382306905 Solving 1.2 + x = 3.382306905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 3.382306905 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 3.382306905 + -1.2 x = 3.382306905 + -1.2 Combine like terms: 3.382306905 + -1.2 = 2.182306905 x = 2.182306905 Simplifying x = 2.182306905Subproblem 2
x + 1.2 = -3.382306905 Simplifying x + 1.2 = -3.382306905 Reorder the terms: 1.2 + x = -3.382306905 Solving 1.2 + x = -3.382306905 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -3.382306905 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -3.382306905 + -1.2 x = -3.382306905 + -1.2 Combine like terms: -3.382306905 + -1.2 = -4.582306905 x = -4.582306905 Simplifying x = -4.582306905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.182306905, -4.582306905}
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