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Simplifying 21x2 + -20x + -48 = 0 Reorder the terms: -48 + -20x + 21x2 = 0 Solving -48 + -20x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -2.285714286 + -0.9523809524x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + -0.9523809524x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + -0.9523809524x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + -0.9523809524x + x2 = 0 + 2.285714286 -0.9523809524x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 -0.9523809524x + x2 = 2.285714286 The x term is -0.9523809524x. Take half its coefficient (-0.4761904762). Square it (0.2267573696) and add it to both sides. Add '0.2267573696' to each side of the equation. -0.9523809524x + 0.2267573696 + x2 = 2.285714286 + 0.2267573696 Reorder the terms: 0.2267573696 + -0.9523809524x + x2 = 2.285714286 + 0.2267573696 Combine like terms: 2.285714286 + 0.2267573696 = 2.5124716556 0.2267573696 + -0.9523809524x + x2 = 2.5124716556 Factor a perfect square on the left side: (x + -0.4761904762)(x + -0.4761904762) = 2.5124716556 Calculate the square root of the right side: 1.585077807 Break this problem into two subproblems by setting (x + -0.4761904762) equal to 1.585077807 and -1.585077807.Subproblem 1
x + -0.4761904762 = 1.585077807 Simplifying x + -0.4761904762 = 1.585077807 Reorder the terms: -0.4761904762 + x = 1.585077807 Solving -0.4761904762 + x = 1.585077807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = 1.585077807 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = 1.585077807 + 0.4761904762 x = 1.585077807 + 0.4761904762 Combine like terms: 1.585077807 + 0.4761904762 = 2.0612682832 x = 2.0612682832 Simplifying x = 2.0612682832Subproblem 2
x + -0.4761904762 = -1.585077807 Simplifying x + -0.4761904762 = -1.585077807 Reorder the terms: -0.4761904762 + x = -1.585077807 Solving -0.4761904762 + x = -1.585077807 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4761904762' to each side of the equation. -0.4761904762 + 0.4761904762 + x = -1.585077807 + 0.4761904762 Combine like terms: -0.4761904762 + 0.4761904762 = 0.0000000000 0.0000000000 + x = -1.585077807 + 0.4761904762 x = -1.585077807 + 0.4761904762 Combine like terms: -1.585077807 + 0.4761904762 = -1.1088873308 x = -1.1088873308 Simplifying x = -1.1088873308Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0612682832, -1.1088873308}
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