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Simplifying 2.1x2 + 6.945x = 10 Reorder the terms: 6.945x + 2.1x2 = 10 Solving 6.945x + 2.1x2 = 10 Solving for variable 'x'. Reorder the terms: -10 + 6.945x + 2.1x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 6.945x + 2.1x2 = 0 Begin completing the square. Divide all terms by 2.1 the coefficient of the squared term: Divide each side by '2.1'. -4.761904762 + 3.307142857x + x2 = 0 Move the constant term to the right: Add '4.761904762' to each side of the equation. -4.761904762 + 3.307142857x + 4.761904762 + x2 = 0 + 4.761904762 Reorder the terms: -4.761904762 + 4.761904762 + 3.307142857x + x2 = 0 + 4.761904762 Combine like terms: -4.761904762 + 4.761904762 = 0.000000000 0.000000000 + 3.307142857x + x2 = 0 + 4.761904762 3.307142857x + x2 = 0 + 4.761904762 Combine like terms: 0 + 4.761904762 = 4.761904762 3.307142857x + x2 = 4.761904762 The x term is 3.307142857x. Take half its coefficient (1.653571429). Square it (2.734298471) and add it to both sides. Add '2.734298471' to each side of the equation. 3.307142857x + 2.734298471 + x2 = 4.761904762 + 2.734298471 Reorder the terms: 2.734298471 + 3.307142857x + x2 = 4.761904762 + 2.734298471 Combine like terms: 4.761904762 + 2.734298471 = 7.496203233 2.734298471 + 3.307142857x + x2 = 7.496203233 Factor a perfect square on the left side: (x + 1.653571429)(x + 1.653571429) = 7.496203233 Calculate the square root of the right side: 2.737919508 Break this problem into two subproblems by setting (x + 1.653571429) equal to 2.737919508 and -2.737919508.Subproblem 1
x + 1.653571429 = 2.737919508 Simplifying x + 1.653571429 = 2.737919508 Reorder the terms: 1.653571429 + x = 2.737919508 Solving 1.653571429 + x = 2.737919508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.653571429' to each side of the equation. 1.653571429 + -1.653571429 + x = 2.737919508 + -1.653571429 Combine like terms: 1.653571429 + -1.653571429 = 0.000000000 0.000000000 + x = 2.737919508 + -1.653571429 x = 2.737919508 + -1.653571429 Combine like terms: 2.737919508 + -1.653571429 = 1.084348079 x = 1.084348079 Simplifying x = 1.084348079Subproblem 2
x + 1.653571429 = -2.737919508 Simplifying x + 1.653571429 = -2.737919508 Reorder the terms: 1.653571429 + x = -2.737919508 Solving 1.653571429 + x = -2.737919508 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.653571429' to each side of the equation. 1.653571429 + -1.653571429 + x = -2.737919508 + -1.653571429 Combine like terms: 1.653571429 + -1.653571429 = 0.000000000 0.000000000 + x = -2.737919508 + -1.653571429 x = -2.737919508 + -1.653571429 Combine like terms: -2.737919508 + -1.653571429 = -4.391490937 x = -4.391490937 Simplifying x = -4.391490937Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.084348079, -4.391490937}
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