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Simplifying 49x2 + -14x = 6 Reorder the terms: -14x + 49x2 = 6 Solving -14x + 49x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -14x + 49x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -14x + 49x2 = 0 Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. -0.1224489796 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '0.1224489796' to each side of the equation. -0.1224489796 + -0.2857142857x + 0.1224489796 + x2 = 0 + 0.1224489796 Reorder the terms: -0.1224489796 + 0.1224489796 + -0.2857142857x + x2 = 0 + 0.1224489796 Combine like terms: -0.1224489796 + 0.1224489796 = 0.0000000000 0.0000000000 + -0.2857142857x + x2 = 0 + 0.1224489796 -0.2857142857x + x2 = 0 + 0.1224489796 Combine like terms: 0 + 0.1224489796 = 0.1224489796 -0.2857142857x + x2 = 0.1224489796 The x term is -0.2857142857x. Take half its coefficient (-0.1428571429). Square it (0.02040816328) and add it to both sides. Add '0.02040816328' to each side of the equation. -0.2857142857x + 0.02040816328 + x2 = 0.1224489796 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 0.1224489796 + 0.02040816328 Combine like terms: 0.1224489796 + 0.02040816328 = 0.14285714288 0.02040816328 + -0.2857142857x + x2 = 0.14285714288 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 0.14285714288 Calculate the square root of the right side: 0.377964473 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 0.377964473 and -0.377964473.Subproblem 1
x + -0.1428571429 = 0.377964473 Simplifying x + -0.1428571429 = 0.377964473 Reorder the terms: -0.1428571429 + x = 0.377964473 Solving -0.1428571429 + x = 0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = 0.377964473 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 0.377964473 + 0.1428571429 x = 0.377964473 + 0.1428571429 Combine like terms: 0.377964473 + 0.1428571429 = 0.5208216159 x = 0.5208216159 Simplifying x = 0.5208216159Subproblem 2
x + -0.1428571429 = -0.377964473 Simplifying x + -0.1428571429 = -0.377964473 Reorder the terms: -0.1428571429 + x = -0.377964473 Solving -0.1428571429 + x = -0.377964473 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1428571429' to each side of the equation. -0.1428571429 + 0.1428571429 + x = -0.377964473 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -0.377964473 + 0.1428571429 x = -0.377964473 + 0.1428571429 Combine like terms: -0.377964473 + 0.1428571429 = -0.2351073301 x = -0.2351073301 Simplifying x = -0.2351073301Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5208216159, -0.2351073301}
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