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Simplifying 25x2 + -80x + 64 = 4(x + 5) Reorder the terms: 64 + -80x + 25x2 = 4(x + 5) Reorder the terms: 64 + -80x + 25x2 = 4(5 + x) 64 + -80x + 25x2 = (5 * 4 + x * 4) 64 + -80x + 25x2 = (20 + 4x) Solving 64 + -80x + 25x2 = 20 + 4x Solving for variable 'x'. Reorder the terms: 64 + -20 + -80x + -4x + 25x2 = 20 + 4x + -20 + -4x Combine like terms: 64 + -20 = 44 44 + -80x + -4x + 25x2 = 20 + 4x + -20 + -4x Combine like terms: -80x + -4x = -84x 44 + -84x + 25x2 = 20 + 4x + -20 + -4x Reorder the terms: 44 + -84x + 25x2 = 20 + -20 + 4x + -4x Combine like terms: 20 + -20 = 0 44 + -84x + 25x2 = 0 + 4x + -4x 44 + -84x + 25x2 = 4x + -4x Combine like terms: 4x + -4x = 0 44 + -84x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.76 + -3.36x + x2 = 0 Move the constant term to the right: Add '-1.76' to each side of the equation. 1.76 + -3.36x + -1.76 + x2 = 0 + -1.76 Reorder the terms: 1.76 + -1.76 + -3.36x + x2 = 0 + -1.76 Combine like terms: 1.76 + -1.76 = 0.00 0.00 + -3.36x + x2 = 0 + -1.76 -3.36x + x2 = 0 + -1.76 Combine like terms: 0 + -1.76 = -1.76 -3.36x + x2 = -1.76 The x term is -3.36x. Take half its coefficient (-1.68). Square it (2.8224) and add it to both sides. Add '2.8224' to each side of the equation. -3.36x + 2.8224 + x2 = -1.76 + 2.8224 Reorder the terms: 2.8224 + -3.36x + x2 = -1.76 + 2.8224 Combine like terms: -1.76 + 2.8224 = 1.0624 2.8224 + -3.36x + x2 = 1.0624 Factor a perfect square on the left side: (x + -1.68)(x + -1.68) = 1.0624 Calculate the square root of the right side: 1.030727898 Break this problem into two subproblems by setting (x + -1.68) equal to 1.030727898 and -1.030727898.Subproblem 1
x + -1.68 = 1.030727898 Simplifying x + -1.68 = 1.030727898 Reorder the terms: -1.68 + x = 1.030727898 Solving -1.68 + x = 1.030727898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.68' to each side of the equation. -1.68 + 1.68 + x = 1.030727898 + 1.68 Combine like terms: -1.68 + 1.68 = 0.00 0.00 + x = 1.030727898 + 1.68 x = 1.030727898 + 1.68 Combine like terms: 1.030727898 + 1.68 = 2.710727898 x = 2.710727898 Simplifying x = 2.710727898Subproblem 2
x + -1.68 = -1.030727898 Simplifying x + -1.68 = -1.030727898 Reorder the terms: -1.68 + x = -1.030727898 Solving -1.68 + x = -1.030727898 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.68' to each side of the equation. -1.68 + 1.68 + x = -1.030727898 + 1.68 Combine like terms: -1.68 + 1.68 = 0.00 0.00 + x = -1.030727898 + 1.68 x = -1.030727898 + 1.68 Combine like terms: -1.030727898 + 1.68 = 0.649272102 x = 0.649272102 Simplifying x = 0.649272102Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.710727898, 0.649272102}
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