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Simplifying 8x2 = 20x + 47 Reorder the terms: 8x2 = 47 + 20x Solving 8x2 = 47 + 20x Solving for variable 'x'. Reorder the terms: -47 + -20x + 8x2 = 47 + 20x + -47 + -20x Reorder the terms: -47 + -20x + 8x2 = 47 + -47 + 20x + -20x Combine like terms: 47 + -47 = 0 -47 + -20x + 8x2 = 0 + 20x + -20x -47 + -20x + 8x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -47 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.875 + -2.5x + x2 = 0 Move the constant term to the right: Add '5.875' to each side of the equation. -5.875 + -2.5x + 5.875 + x2 = 0 + 5.875 Reorder the terms: -5.875 + 5.875 + -2.5x + x2 = 0 + 5.875 Combine like terms: -5.875 + 5.875 = 0.000 0.000 + -2.5x + x2 = 0 + 5.875 -2.5x + x2 = 0 + 5.875 Combine like terms: 0 + 5.875 = 5.875 -2.5x + x2 = 5.875 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 5.875 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 5.875 + 1.5625 Combine like terms: 5.875 + 1.5625 = 7.4375 1.5625 + -2.5x + x2 = 7.4375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.4375 Calculate the square root of the right side: 2.727178029 Break this problem into two subproblems by setting (x + -1.25) equal to 2.727178029 and -2.727178029.Subproblem 1
x + -1.25 = 2.727178029 Simplifying x + -1.25 = 2.727178029 Reorder the terms: -1.25 + x = 2.727178029 Solving -1.25 + x = 2.727178029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.727178029 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.727178029 + 1.25 x = 2.727178029 + 1.25 Combine like terms: 2.727178029 + 1.25 = 3.977178029 x = 3.977178029 Simplifying x = 3.977178029Subproblem 2
x + -1.25 = -2.727178029 Simplifying x + -1.25 = -2.727178029 Reorder the terms: -1.25 + x = -2.727178029 Solving -1.25 + x = -2.727178029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.727178029 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.727178029 + 1.25 x = -2.727178029 + 1.25 Combine like terms: -2.727178029 + 1.25 = -1.477178029 x = -1.477178029 Simplifying x = -1.477178029Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.977178029, -1.477178029}
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