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Simplifying 48x2 + -8x + -3 = 0 Reorder the terms: -3 + -8x + 48x2 = 0 Solving -3 + -8x + 48x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 48 the coefficient of the squared term: Divide each side by '48'. -0.0625 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.1666666667x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.1666666667x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.1666666667x + x2 = 0 + 0.0625 -0.1666666667x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.1666666667x + x2 = 0.0625 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.0625 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.0625 + 0.006944444447 Combine like terms: 0.0625 + 0.006944444447 = 0.069444444447 0.006944444447 + -0.1666666667x + x2 = 0.069444444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.069444444447 Calculate the square root of the right side: 0.263523138 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.263523138 and -0.263523138.Subproblem 1
x + -0.08333333335 = 0.263523138 Simplifying x + -0.08333333335 = 0.263523138 Reorder the terms: -0.08333333335 + x = 0.263523138 Solving -0.08333333335 + x = 0.263523138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.263523138 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.263523138 + 0.08333333335 x = 0.263523138 + 0.08333333335 Combine like terms: 0.263523138 + 0.08333333335 = 0.34685647135 x = 0.34685647135 Simplifying x = 0.34685647135Subproblem 2
x + -0.08333333335 = -0.263523138 Simplifying x + -0.08333333335 = -0.263523138 Reorder the terms: -0.08333333335 + x = -0.263523138 Solving -0.08333333335 + x = -0.263523138 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.263523138 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.263523138 + 0.08333333335 x = -0.263523138 + 0.08333333335 Combine like terms: -0.263523138 + 0.08333333335 = -0.18018980465 x = -0.18018980465 Simplifying x = -0.18018980465Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.34685647135, -0.18018980465}
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