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Simplifying 21x2 + 20x + 3 = 0 Reorder the terms: 3 + 20x + 21x2 = 0 Solving 3 + 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'. 0.1428571429 + 0.9523809524x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + 0.9523809524x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + 0.9523809524x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + 0.9523809524x + x2 = 0 + -0.1428571429 0.9523809524x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 0.9523809524x + x2 = -0.1428571429 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 = -0.1428571429 + 0.2267573696 Reorder the terms: 0.2267573696 + 0.9523809524x + x2 = -0.1428571429 + 0.2267573696 Combine like terms: -0.1428571429 + 0.2267573696 = 0.0839002267 0.2267573696 + 0.9523809524x + x2 = 0.0839002267 Factor a perfect square on the left side: (x + 0.4761904762)(x + 0.4761904762) = 0.0839002267 Calculate the square root of the right side: 0.289655358 Break this problem into two subproblems by setting (x + 0.4761904762) equal to 0.289655358 and -0.289655358.Subproblem 1
x + 0.4761904762 = 0.289655358 Simplifying x + 0.4761904762 = 0.289655358 Reorder the terms: 0.4761904762 + x = 0.289655358 Solving 0.4761904762 + x = 0.289655358 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 = 0.289655358 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + x = 0.289655358 + -0.4761904762 x = 0.289655358 + -0.4761904762 Combine like terms: 0.289655358 + -0.4761904762 = -0.1865351182 x = -0.1865351182 Simplifying x = -0.1865351182Subproblem 2
x + 0.4761904762 = -0.289655358 Simplifying x + 0.4761904762 = -0.289655358 Reorder the terms: 0.4761904762 + x = -0.289655358 Solving 0.4761904762 + x = -0.289655358 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 = -0.289655358 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + x = -0.289655358 + -0.4761904762 x = -0.289655358 + -0.4761904762 Combine like terms: -0.289655358 + -0.4761904762 = -0.7658458342 x = -0.7658458342 Simplifying x = -0.7658458342Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1865351182, -0.7658458342}
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