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Simplifying 4x2 + 195x + -24600 = 0 Reorder the terms: -24600 + 195x + 4x2 = 0 Solving -24600 + 195x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6150 + 48.75x + x2 = 0 Move the constant term to the right: Add '6150' to each side of the equation. -6150 + 48.75x + 6150 + x2 = 0 + 6150 Reorder the terms: -6150 + 6150 + 48.75x + x2 = 0 + 6150 Combine like terms: -6150 + 6150 = 0 0 + 48.75x + x2 = 0 + 6150 48.75x + x2 = 0 + 6150 Combine like terms: 0 + 6150 = 6150 48.75x + x2 = 6150 The x term is 48.75x. Take half its coefficient (24.375). Square it (594.140625) and add it to both sides. Add '594.140625' to each side of the equation. 48.75x + 594.140625 + x2 = 6150 + 594.140625 Reorder the terms: 594.140625 + 48.75x + x2 = 6150 + 594.140625 Combine like terms: 6150 + 594.140625 = 6744.140625 594.140625 + 48.75x + x2 = 6744.140625 Factor a perfect square on the left side: (x + 24.375)(x + 24.375) = 6744.140625 Calculate the square root of the right side: 82.122716863 Break this problem into two subproblems by setting (x + 24.375) equal to 82.122716863 and -82.122716863.Subproblem 1
x + 24.375 = 82.122716863 Simplifying x + 24.375 = 82.122716863 Reorder the terms: 24.375 + x = 82.122716863 Solving 24.375 + x = 82.122716863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.375' to each side of the equation. 24.375 + -24.375 + x = 82.122716863 + -24.375 Combine like terms: 24.375 + -24.375 = 0.000 0.000 + x = 82.122716863 + -24.375 x = 82.122716863 + -24.375 Combine like terms: 82.122716863 + -24.375 = 57.747716863 x = 57.747716863 Simplifying x = 57.747716863Subproblem 2
x + 24.375 = -82.122716863 Simplifying x + 24.375 = -82.122716863 Reorder the terms: 24.375 + x = -82.122716863 Solving 24.375 + x = -82.122716863 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-24.375' to each side of the equation. 24.375 + -24.375 + x = -82.122716863 + -24.375 Combine like terms: 24.375 + -24.375 = 0.000 0.000 + x = -82.122716863 + -24.375 x = -82.122716863 + -24.375 Combine like terms: -82.122716863 + -24.375 = -106.497716863 x = -106.497716863 Simplifying x = -106.497716863Solution
The solution to the problem is based on the solutions from the subproblems. x = {57.747716863, -106.497716863}
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