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Simplifying -4.905x2 + 11x + -0.4 = 0 Reorder the terms: -0.4 + 11x + -4.905x2 = 0 Solving -0.4 + 11x + -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'. 0.08154943935 + -2.242609582x + x2 = 0 Move the constant term to the right: Add '-0.08154943935' to each side of the equation. 0.08154943935 + -2.242609582x + -0.08154943935 + x2 = 0 + -0.08154943935 Reorder the terms: 0.08154943935 + -0.08154943935 + -2.242609582x + x2 = 0 + -0.08154943935 Combine like terms: 0.08154943935 + -0.08154943935 = 0.00000000000 0.00000000000 + -2.242609582x + x2 = 0 + -0.08154943935 -2.242609582x + x2 = 0 + -0.08154943935 Combine like terms: 0 + -0.08154943935 = -0.08154943935 -2.242609582x + x2 = -0.08154943935 The x term is -2.242609582x. Take half its coefficient (-1.121304791). Square it (1.257324434) and add it to both sides. Add '1.257324434' to each side of the equation. -2.242609582x + 1.257324434 + x2 = -0.08154943935 + 1.257324434 Reorder the terms: 1.257324434 + -2.242609582x + x2 = -0.08154943935 + 1.257324434 Combine like terms: -0.08154943935 + 1.257324434 = 1.17577499465 1.257324434 + -2.242609582x + x2 = 1.17577499465 Factor a perfect square on the left side: (x + -1.121304791)(x + -1.121304791) = 1.17577499465 Calculate the square root of the right side: 1.084331589 Break this problem into two subproblems by setting (x + -1.121304791) equal to 1.084331589 and -1.084331589.Subproblem 1
x + -1.121304791 = 1.084331589 Simplifying x + -1.121304791 = 1.084331589 Reorder the terms: -1.121304791 + x = 1.084331589 Solving -1.121304791 + x = 1.084331589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.121304791' to each side of the equation. -1.121304791 + 1.121304791 + x = 1.084331589 + 1.121304791 Combine like terms: -1.121304791 + 1.121304791 = 0.000000000 0.000000000 + x = 1.084331589 + 1.121304791 x = 1.084331589 + 1.121304791 Combine like terms: 1.084331589 + 1.121304791 = 2.20563638 x = 2.20563638 Simplifying x = 2.20563638Subproblem 2
x + -1.121304791 = -1.084331589 Simplifying x + -1.121304791 = -1.084331589 Reorder the terms: -1.121304791 + x = -1.084331589 Solving -1.121304791 + x = -1.084331589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.121304791' to each side of the equation. -1.121304791 + 1.121304791 + x = -1.084331589 + 1.121304791 Combine like terms: -1.121304791 + 1.121304791 = 0.000000000 0.000000000 + x = -1.084331589 + 1.121304791 x = -1.084331589 + 1.121304791 Combine like terms: -1.084331589 + 1.121304791 = 0.036973202 x = 0.036973202 Simplifying x = 0.036973202Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.20563638, 0.036973202}
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