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Simplifying 21x2 + 2x + -0.09 = 0 Reorder the terms: -0.09 + 2x + 21x2 = 0 Solving -0.09 + 2x + 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'. -0.004285714286 + 0.09523809524x + x2 = 0 Move the constant term to the right: Add '0.004285714286' to each side of the equation. -0.004285714286 + 0.09523809524x + 0.004285714286 + x2 = 0 + 0.004285714286 Reorder the terms: -0.004285714286 + 0.004285714286 + 0.09523809524x + x2 = 0 + 0.004285714286 Combine like terms: -0.004285714286 + 0.004285714286 = 0.000000000000 0.000000000000 + 0.09523809524x + x2 = 0 + 0.004285714286 0.09523809524x + x2 = 0 + 0.004285714286 Combine like terms: 0 + 0.004285714286 = 0.004285714286 0.09523809524x + x2 = 0.004285714286 The x term is 0.09523809524x. 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. 0.09523809524x + 0.002267573696 + x2 = 0.004285714286 + 0.002267573696 Reorder the terms: 0.002267573696 + 0.09523809524x + x2 = 0.004285714286 + 0.002267573696 Combine like terms: 0.004285714286 + 0.002267573696 = 0.006553287982 0.002267573696 + 0.09523809524x + x2 = 0.006553287982 Factor a perfect square on the left side: (x + 0.04761904762)(x + 0.04761904762) = 0.006553287982 Calculate the square root of the right side: 0.080952381 Break this problem into two subproblems by setting (x + 0.04761904762) equal to 0.080952381 and -0.080952381.Subproblem 1
x + 0.04761904762 = 0.080952381 Simplifying x + 0.04761904762 = 0.080952381 Reorder the terms: 0.04761904762 + x = 0.080952381 Solving 0.04761904762 + x = 0.080952381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = 0.080952381 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = 0.080952381 + -0.04761904762 x = 0.080952381 + -0.04761904762 Combine like terms: 0.080952381 + -0.04761904762 = 0.03333333338 x = 0.03333333338 Simplifying x = 0.03333333338Subproblem 2
x + 0.04761904762 = -0.080952381 Simplifying x + 0.04761904762 = -0.080952381 Reorder the terms: 0.04761904762 + x = -0.080952381 Solving 0.04761904762 + x = -0.080952381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.04761904762' to each side of the equation. 0.04761904762 + -0.04761904762 + x = -0.080952381 + -0.04761904762 Combine like terms: 0.04761904762 + -0.04761904762 = 0.00000000000 0.00000000000 + x = -0.080952381 + -0.04761904762 x = -0.080952381 + -0.04761904762 Combine like terms: -0.080952381 + -0.04761904762 = -0.12857142862 x = -0.12857142862 Simplifying x = -0.12857142862Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.03333333338, -0.12857142862}
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