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Simplifying 11x + -4.9x2 + 22 = 0 Reorder the terms: 22 + 11x + -4.9x2 = 0 Solving 22 + 11x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -4.489795918 + -2.244897959x + x2 = 0 Move the constant term to the right: Add '4.489795918' to each side of the equation. -4.489795918 + -2.244897959x + 4.489795918 + x2 = 0 + 4.489795918 Reorder the terms: -4.489795918 + 4.489795918 + -2.244897959x + x2 = 0 + 4.489795918 Combine like terms: -4.489795918 + 4.489795918 = 0.000000000 0.000000000 + -2.244897959x + x2 = 0 + 4.489795918 -2.244897959x + x2 = 0 + 4.489795918 Combine like terms: 0 + 4.489795918 = 4.489795918 -2.244897959x + x2 = 4.489795918 The x term is -2.244897959x. Take half its coefficient (-1.12244898). Square it (1.259891713) and add it to both sides. Add '1.259891713' to each side of the equation. -2.244897959x + 1.259891713 + x2 = 4.489795918 + 1.259891713 Reorder the terms: 1.259891713 + -2.244897959x + x2 = 4.489795918 + 1.259891713 Combine like terms: 4.489795918 + 1.259891713 = 5.749687631 1.259891713 + -2.244897959x + x2 = 5.749687631 Factor a perfect square on the left side: (x + -1.12244898)(x + -1.12244898) = 5.749687631 Calculate the square root of the right side: 2.397850627 Break this problem into two subproblems by setting (x + -1.12244898) equal to 2.397850627 and -2.397850627.Subproblem 1
x + -1.12244898 = 2.397850627 Simplifying x + -1.12244898 = 2.397850627 Reorder the terms: -1.12244898 + x = 2.397850627 Solving -1.12244898 + x = 2.397850627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = 2.397850627 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = 2.397850627 + 1.12244898 x = 2.397850627 + 1.12244898 Combine like terms: 2.397850627 + 1.12244898 = 3.520299607 x = 3.520299607 Simplifying x = 3.520299607Subproblem 2
x + -1.12244898 = -2.397850627 Simplifying x + -1.12244898 = -2.397850627 Reorder the terms: -1.12244898 + x = -2.397850627 Solving -1.12244898 + x = -2.397850627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.12244898' to each side of the equation. -1.12244898 + 1.12244898 + x = -2.397850627 + 1.12244898 Combine like terms: -1.12244898 + 1.12244898 = 0.00000000 0.00000000 + x = -2.397850627 + 1.12244898 x = -2.397850627 + 1.12244898 Combine like terms: -2.397850627 + 1.12244898 = -1.275401647 x = -1.275401647 Simplifying x = -1.275401647Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.520299607, -1.275401647}
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