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Simplifying 8x2 = 20x + 43 Reorder the terms: 8x2 = 43 + 20x Solving 8x2 = 43 + 20x Solving for variable 'x'. Reorder the terms: -43 + -20x + 8x2 = 43 + 20x + -43 + -20x Reorder the terms: -43 + -20x + 8x2 = 43 + -43 + 20x + -20x Combine like terms: 43 + -43 = 0 -43 + -20x + 8x2 = 0 + 20x + -20x -43 + -20x + 8x2 = 20x + -20x Combine like terms: 20x + -20x = 0 -43 + -20x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.375 + -2.5x + x2 = 0 Move the constant term to the right: Add '5.375' to each side of the equation. -5.375 + -2.5x + 5.375 + x2 = 0 + 5.375 Reorder the terms: -5.375 + 5.375 + -2.5x + x2 = 0 + 5.375 Combine like terms: -5.375 + 5.375 = 0.000 0.000 + -2.5x + x2 = 0 + 5.375 -2.5x + x2 = 0 + 5.375 Combine like terms: 0 + 5.375 = 5.375 -2.5x + x2 = 5.375 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 = 5.375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 5.375 + 1.5625 Combine like terms: 5.375 + 1.5625 = 6.9375 1.5625 + -2.5x + x2 = 6.9375 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 6.9375 Calculate the square root of the right side: 2.633913438 Break this problem into two subproblems by setting (x + -1.25) equal to 2.633913438 and -2.633913438.Subproblem 1
x + -1.25 = 2.633913438 Simplifying x + -1.25 = 2.633913438 Reorder the terms: -1.25 + x = 2.633913438 Solving -1.25 + x = 2.633913438 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 = 2.633913438 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.633913438 + 1.25 x = 2.633913438 + 1.25 Combine like terms: 2.633913438 + 1.25 = 3.883913438 x = 3.883913438 Simplifying x = 3.883913438Subproblem 2
x + -1.25 = -2.633913438 Simplifying x + -1.25 = -2.633913438 Reorder the terms: -1.25 + x = -2.633913438 Solving -1.25 + x = -2.633913438 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 = -2.633913438 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.633913438 + 1.25 x = -2.633913438 + 1.25 Combine like terms: -2.633913438 + 1.25 = -1.383913438 x = -1.383913438 Simplifying x = -1.383913438Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.883913438, -1.383913438}
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