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Simplifying 5 + -2w = 21w2 Solving 5 + -2w = 21w2 Solving for variable 'w'. Combine like terms: 21w2 + -21w2 = 0 5 + -2w + -21w2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. -0.2380952381 + 0.09523809524w + w2 = 0 Move the constant term to the right: Add '0.2380952381' to each side of the equation. -0.2380952381 + 0.09523809524w + 0.2380952381 + w2 = 0 + 0.2380952381 Reorder the terms: -0.2380952381 + 0.2380952381 + 0.09523809524w + w2 = 0 + 0.2380952381 Combine like terms: -0.2380952381 + 0.2380952381 = 0.0000000000 0.0000000000 + 0.09523809524w + w2 = 0 + 0.2380952381 0.09523809524w + w2 = 0 + 0.2380952381 Combine like terms: 0 + 0.2380952381 = 0.2380952381 0.09523809524w + w2 = 0.2380952381 The w term is 0.09523809524w. Take half its coefficient (0.04761904762). Square it (0.002267573696) and add it to both sides. Add '0.002267573696' to each side of the equation. 0.09523809524w + 0.002267573696 + w2 = 0.2380952381 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524w + w2 = 0.2380952381 + 0.002267573696 Combine like terms: 0.2380952381 + 0.002267573696 = 0.240362811796 0.002267573696 + 0.09523809524w + w2 = 0.240362811796 Factor a perfect square on the left side: (w + 0.04761904762)(w + 0.04761904762) = 0.240362811796 Calculate the square root of the right side: 0.490268102 Break this problem into two subproblems by setting (w + 0.04761904762) equal to 0.490268102 and -0.490268102.Subproblem 1
w + 0.04761904762 = 0.490268102 Simplifying w + 0.04761904762 = 0.490268102 Reorder the terms: 0.04761904762 + w = 0.490268102 Solving 0.04761904762 + w = 0.490268102 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + w = 0.490268102 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + w = 0.490268102 + -0.04761904762 w = 0.490268102 + -0.04761904762 Combine like terms: 0.490268102 + -0.04761904762 = 0.44264905438 w = 0.44264905438 Simplifying w = 0.44264905438Subproblem 2
w + 0.04761904762 = -0.490268102 Simplifying w + 0.04761904762 = -0.490268102 Reorder the terms: 0.04761904762 + w = -0.490268102 Solving 0.04761904762 + w = -0.490268102 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + w = -0.490268102 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + w = -0.490268102 + -0.04761904762 w = -0.490268102 + -0.04761904762 Combine like terms: -0.490268102 + -0.04761904762 = -0.53788714962 w = -0.53788714962 Simplifying w = -0.53788714962Solution
The solution to the problem is based on the solutions from the subproblems. w = {0.44264905438, -0.53788714962}
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