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Simplifying 5x(5x + 8) = 81 Reorder the terms: 5x(8 + 5x) = 81 (8 * 5x + 5x * 5x) = 81 (40x + 25x2) = 81 Solving 40x + 25x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 40x + 25x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 40x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -3.24 + 1.6x + x2 = 0 Move the constant term to the right: Add '3.24' to each side of the equation. -3.24 + 1.6x + 3.24 + x2 = 0 + 3.24 Reorder the terms: -3.24 + 3.24 + 1.6x + x2 = 0 + 3.24 Combine like terms: -3.24 + 3.24 = 0.00 0.00 + 1.6x + x2 = 0 + 3.24 1.6x + x2 = 0 + 3.24 Combine like terms: 0 + 3.24 = 3.24 1.6x + x2 = 3.24 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 3.24 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 3.24 + 0.64 Combine like terms: 3.24 + 0.64 = 3.88 0.64 + 1.6x + x2 = 3.88 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 3.88 Calculate the square root of the right side: 1.96977156 Break this problem into two subproblems by setting (x + 0.8) equal to 1.96977156 and -1.96977156.Subproblem 1
x + 0.8 = 1.96977156 Simplifying x + 0.8 = 1.96977156 Reorder the terms: 0.8 + x = 1.96977156 Solving 0.8 + x = 1.96977156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 1.96977156 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 1.96977156 + -0.8 x = 1.96977156 + -0.8 Combine like terms: 1.96977156 + -0.8 = 1.16977156 x = 1.16977156 Simplifying x = 1.16977156Subproblem 2
x + 0.8 = -1.96977156 Simplifying x + 0.8 = -1.96977156 Reorder the terms: 0.8 + x = -1.96977156 Solving 0.8 + x = -1.96977156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -1.96977156 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -1.96977156 + -0.8 x = -1.96977156 + -0.8 Combine like terms: -1.96977156 + -0.8 = -2.76977156 x = -2.76977156 Simplifying x = -2.76977156Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.16977156, -2.76977156}
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