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Simplifying 4x2 + -1x + -2304 = 0 Reorder the terms: -2304 + -1x + 4x2 = 0 Solving -2304 + -1x + 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'. -576 + -0.25x + x2 = 0 Move the constant term to the right: Add '576' to each side of the equation. -576 + -0.25x + 576 + x2 = 0 + 576 Reorder the terms: -576 + 576 + -0.25x + x2 = 0 + 576 Combine like terms: -576 + 576 = 0 0 + -0.25x + x2 = 0 + 576 -0.25x + x2 = 0 + 576 Combine like terms: 0 + 576 = 576 -0.25x + x2 = 576 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 576 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 576 + 0.015625 Combine like terms: 576 + 0.015625 = 576.015625 0.015625 + -0.25x + x2 = 576.015625 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 576.015625 Calculate the square root of the right side: 24.000325519 Break this problem into two subproblems by setting (x + -0.125) equal to 24.000325519 and -24.000325519.Subproblem 1
x + -0.125 = 24.000325519 Simplifying x + -0.125 = 24.000325519 Reorder the terms: -0.125 + x = 24.000325519 Solving -0.125 + x = 24.000325519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 24.000325519 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 24.000325519 + 0.125 x = 24.000325519 + 0.125 Combine like terms: 24.000325519 + 0.125 = 24.125325519 x = 24.125325519 Simplifying x = 24.125325519Subproblem 2
x + -0.125 = -24.000325519 Simplifying x + -0.125 = -24.000325519 Reorder the terms: -0.125 + x = -24.000325519 Solving -0.125 + x = -24.000325519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -24.000325519 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -24.000325519 + 0.125 x = -24.000325519 + 0.125 Combine like terms: -24.000325519 + 0.125 = -23.875325519 x = -23.875325519 Simplifying x = -23.875325519Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.125325519, -23.875325519}
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