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Simplifying 4.905x2 + -43.05x + -44 = 0 Reorder the terms: -44 + -43.05x + 4.905x2 = 0 Solving -44 + -43.05x + 4.905x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.905 the coefficient of the squared term: Divide each side by '4.905'. -8.970438328 + -8.77675841x + x2 = 0 Move the constant term to the right: Add '8.970438328' to each side of the equation. -8.970438328 + -8.77675841x + 8.970438328 + x2 = 0 + 8.970438328 Reorder the terms: -8.970438328 + 8.970438328 + -8.77675841x + x2 = 0 + 8.970438328 Combine like terms: -8.970438328 + 8.970438328 = 0.000000000 0.000000000 + -8.77675841x + x2 = 0 + 8.970438328 -8.77675841x + x2 = 0 + 8.970438328 Combine like terms: 0 + 8.970438328 = 8.970438328 -8.77675841x + x2 = 8.970438328 The x term is -8.77675841x. Take half its coefficient (-4.388379205). Square it (19.25787205) and add it to both sides. Add '19.25787205' to each side of the equation. -8.77675841x + 19.25787205 + x2 = 8.970438328 + 19.25787205 Reorder the terms: 19.25787205 + -8.77675841x + x2 = 8.970438328 + 19.25787205 Combine like terms: 8.970438328 + 19.25787205 = 28.228310378 19.25787205 + -8.77675841x + x2 = 28.228310378 Factor a perfect square on the left side: (x + -4.388379205)(x + -4.388379205) = 28.228310378 Calculate the square root of the right side: 5.313032127 Break this problem into two subproblems by setting (x + -4.388379205) equal to 5.313032127 and -5.313032127.Subproblem 1
x + -4.388379205 = 5.313032127 Simplifying x + -4.388379205 = 5.313032127 Reorder the terms: -4.388379205 + x = 5.313032127 Solving -4.388379205 + x = 5.313032127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.388379205' to each side of the equation. -4.388379205 + 4.388379205 + x = 5.313032127 + 4.388379205 Combine like terms: -4.388379205 + 4.388379205 = 0.000000000 0.000000000 + x = 5.313032127 + 4.388379205 x = 5.313032127 + 4.388379205 Combine like terms: 5.313032127 + 4.388379205 = 9.701411332 x = 9.701411332 Simplifying x = 9.701411332Subproblem 2
x + -4.388379205 = -5.313032127 Simplifying x + -4.388379205 = -5.313032127 Reorder the terms: -4.388379205 + x = -5.313032127 Solving -4.388379205 + x = -5.313032127 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.388379205' to each side of the equation. -4.388379205 + 4.388379205 + x = -5.313032127 + 4.388379205 Combine like terms: -4.388379205 + 4.388379205 = 0.000000000 0.000000000 + x = -5.313032127 + 4.388379205 x = -5.313032127 + 4.388379205 Combine like terms: -5.313032127 + 4.388379205 = -0.924652922 x = -0.924652922 Simplifying x = -0.924652922Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.701411332, -0.924652922}
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