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Simplifying 7x2 + -2x + -3 = 44 Reorder the terms: -3 + -2x + 7x2 = 44 Solving -3 + -2x + 7x2 = 44 Solving for variable 'x'. Reorder the terms: -3 + -44 + -2x + 7x2 = 44 + -44 Combine like terms: -3 + -44 = -47 -47 + -2x + 7x2 = 44 + -44 Combine like terms: 44 + -44 = 0 -47 + -2x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -6.714285714 + -0.2857142857x + x2 = 0 Move the constant term to the right: Add '6.714285714' to each side of the equation. -6.714285714 + -0.2857142857x + 6.714285714 + x2 = 0 + 6.714285714 Reorder the terms: -6.714285714 + 6.714285714 + -0.2857142857x + x2 = 0 + 6.714285714 Combine like terms: -6.714285714 + 6.714285714 = 0.000000000 0.000000000 + -0.2857142857x + x2 = 0 + 6.714285714 -0.2857142857x + x2 = 0 + 6.714285714 Combine like terms: 0 + 6.714285714 = 6.714285714 -0.2857142857x + x2 = 6.714285714 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 = 6.714285714 + 0.02040816328 Reorder the terms: 0.02040816328 + -0.2857142857x + x2 = 6.714285714 + 0.02040816328 Combine like terms: 6.714285714 + 0.02040816328 = 6.73469387728 0.02040816328 + -0.2857142857x + x2 = 6.73469387728 Factor a perfect square on the left side: (x + -0.1428571429)(x + -0.1428571429) = 6.73469387728 Calculate the square root of the right side: 2.595128875 Break this problem into two subproblems by setting (x + -0.1428571429) equal to 2.595128875 and -2.595128875.Subproblem 1
x + -0.1428571429 = 2.595128875 Simplifying x + -0.1428571429 = 2.595128875 Reorder the terms: -0.1428571429 + x = 2.595128875 Solving -0.1428571429 + x = 2.595128875 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 = 2.595128875 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = 2.595128875 + 0.1428571429 x = 2.595128875 + 0.1428571429 Combine like terms: 2.595128875 + 0.1428571429 = 2.7379860179 x = 2.7379860179 Simplifying x = 2.7379860179Subproblem 2
x + -0.1428571429 = -2.595128875 Simplifying x + -0.1428571429 = -2.595128875 Reorder the terms: -0.1428571429 + x = -2.595128875 Solving -0.1428571429 + x = -2.595128875 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 = -2.595128875 + 0.1428571429 Combine like terms: -0.1428571429 + 0.1428571429 = 0.0000000000 0.0000000000 + x = -2.595128875 + 0.1428571429 x = -2.595128875 + 0.1428571429 Combine like terms: -2.595128875 + 0.1428571429 = -2.4522717321 x = -2.4522717321 Simplifying x = -2.4522717321Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.7379860179, -2.4522717321}
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