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Simplifying 24x2 + 46x + -65 = 0 Reorder the terms: -65 + 46x + 24x2 = 0 Solving -65 + 46x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -2.708333333 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '2.708333333' to each side of the equation. -2.708333333 + 1.916666667x + 2.708333333 + x2 = 0 + 2.708333333 Reorder the terms: -2.708333333 + 2.708333333 + 1.916666667x + x2 = 0 + 2.708333333 Combine like terms: -2.708333333 + 2.708333333 = 0.000000000 0.000000000 + 1.916666667x + x2 = 0 + 2.708333333 1.916666667x + x2 = 0 + 2.708333333 Combine like terms: 0 + 2.708333333 = 2.708333333 1.916666667x + x2 = 2.708333333 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = 2.708333333 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = 2.708333333 + 0.9184027781 Combine like terms: 2.708333333 + 0.9184027781 = 3.6267361111 0.9184027781 + 1.916666667x + x2 = 3.6267361111 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = 3.6267361111 Calculate the square root of the right side: 1.904399147 Break this problem into two subproblems by setting (x + 0.9583333335) equal to 1.904399147 and -1.904399147.Subproblem 1
x + 0.9583333335 = 1.904399147 Simplifying x + 0.9583333335 = 1.904399147 Reorder the terms: 0.9583333335 + x = 1.904399147 Solving 0.9583333335 + x = 1.904399147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = 1.904399147 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 1.904399147 + -0.9583333335 x = 1.904399147 + -0.9583333335 Combine like terms: 1.904399147 + -0.9583333335 = 0.9460658135 x = 0.9460658135 Simplifying x = 0.9460658135Subproblem 2
x + 0.9583333335 = -1.904399147 Simplifying x + 0.9583333335 = -1.904399147 Reorder the terms: 0.9583333335 + x = -1.904399147 Solving 0.9583333335 + x = -1.904399147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = -1.904399147 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -1.904399147 + -0.9583333335 x = -1.904399147 + -0.9583333335 Combine like terms: -1.904399147 + -0.9583333335 = -2.8627324805 x = -2.8627324805 Simplifying x = -2.8627324805Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9460658135, -2.8627324805}
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