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Simplifying 8x2 = 20x + 45 Reorder the terms: 8x2 = 45 + 20x Solving 8x2 = 45 + 20x Solving for variable 'x'. Reorder the terms: -45 + -20x + 8x2 = 45 + 20x + -45 + -20x Reorder the terms: -45 + -20x + 8x2 = 45 + -45 + 20x + -20x Combine like terms: 45 + -45 = 0 -45 + -20x + 8x2 = 0 + 20x + -20x -45 + -20x + 8x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -45 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.625 + -2.5x + x2 = 0 Move the constant term to the right: Add '5.625' to each side of the equation. -5.625 + -2.5x + 5.625 + x2 = 0 + 5.625 Reorder the terms: -5.625 + 5.625 + -2.5x + x2 = 0 + 5.625 Combine like terms: -5.625 + 5.625 = 0.000 0.000 + -2.5x + x2 = 0 + 5.625 -2.5x + x2 = 0 + 5.625 Combine like terms: 0 + 5.625 = 5.625 -2.5x + x2 = 5.625 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 = 5.625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 5.625 + 1.5625 Combine like terms: 5.625 + 1.5625 = 7.1875 1.5625 + -2.5x + x2 = 7.1875 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.1875 Calculate the square root of the right side: 2.680951324 Break this problem into two subproblems by setting (x + -1.25) equal to 2.680951324 and -2.680951324.Subproblem 1
x + -1.25 = 2.680951324 Simplifying x + -1.25 = 2.680951324 Reorder the terms: -1.25 + x = 2.680951324 Solving -1.25 + x = 2.680951324 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 = 2.680951324 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.680951324 + 1.25 x = 2.680951324 + 1.25 Combine like terms: 2.680951324 + 1.25 = 3.930951324 x = 3.930951324 Simplifying x = 3.930951324Subproblem 2
x + -1.25 = -2.680951324 Simplifying x + -1.25 = -2.680951324 Reorder the terms: -1.25 + x = -2.680951324 Solving -1.25 + x = -2.680951324 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 = -2.680951324 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.680951324 + 1.25 x = -2.680951324 + 1.25 Combine like terms: -2.680951324 + 1.25 = -1.430951324 x = -1.430951324 Simplifying x = -1.430951324Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.930951324, -1.430951324}
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