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Simplifying x2 + 20x2 + 16x + -1 = 0 Reorder the terms: -1 + 16x + x2 + 20x2 = 0 Combine like terms: x2 + 20x2 = 21x2 -1 + 16x + 21x2 = 0 Solving -1 + 16x + 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'. -0.04761904762 + 0.7619047619x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + 0.7619047619x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + 0.7619047619x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + 0.7619047619x + x2 = 0 + 0.04761904762 0.7619047619x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 0.7619047619x + x2 = 0.04761904762 The x term is 0.7619047619x. Take half its coefficient (0.380952381). Square it (0.1451247166) and add it to both sides. Add '0.1451247166' to each side of the equation. 0.7619047619x + 0.1451247166 + x2 = 0.04761904762 + 0.1451247166 Reorder the terms: 0.1451247166 + 0.7619047619x + x2 = 0.04761904762 + 0.1451247166 Combine like terms: 0.04761904762 + 0.1451247166 = 0.19274376422 0.1451247166 + 0.7619047619x + x2 = 0.19274376422 Factor a perfect square on the left side: (x + 0.380952381)(x + 0.380952381) = 0.19274376422 Calculate the square root of the right side: 0.439025927 Break this problem into two subproblems by setting (x + 0.380952381) equal to 0.439025927 and -0.439025927.Subproblem 1
x + 0.380952381 = 0.439025927 Simplifying x + 0.380952381 = 0.439025927 Reorder the terms: 0.380952381 + x = 0.439025927 Solving 0.380952381 + x = 0.439025927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.380952381' to each side of the equation. 0.380952381 + -0.380952381 + x = 0.439025927 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + x = 0.439025927 + -0.380952381 x = 0.439025927 + -0.380952381 Combine like terms: 0.439025927 + -0.380952381 = 0.058073546 x = 0.058073546 Simplifying x = 0.058073546Subproblem 2
x + 0.380952381 = -0.439025927 Simplifying x + 0.380952381 = -0.439025927 Reorder the terms: 0.380952381 + x = -0.439025927 Solving 0.380952381 + x = -0.439025927 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.380952381' to each side of the equation. 0.380952381 + -0.380952381 + x = -0.439025927 + -0.380952381 Combine like terms: 0.380952381 + -0.380952381 = 0.000000000 0.000000000 + x = -0.439025927 + -0.380952381 x = -0.439025927 + -0.380952381 Combine like terms: -0.439025927 + -0.380952381 = -0.819978308 x = -0.819978308 Simplifying x = -0.819978308Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.058073546, -0.819978308}
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