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Simplifying -4.905x2 + 22x + -6 = 0 Reorder the terms: -6 + 22x + -4.905x2 = 0 Solving -6 + 22x + -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'. 1.22324159 + -4.485219164x + x2 = 0 Move the constant term to the right: Add '-1.22324159' to each side of the equation. 1.22324159 + -4.485219164x + -1.22324159 + x2 = 0 + -1.22324159 Reorder the terms: 1.22324159 + -1.22324159 + -4.485219164x + x2 = 0 + -1.22324159 Combine like terms: 1.22324159 + -1.22324159 = 0.00000000 0.00000000 + -4.485219164x + x2 = 0 + -1.22324159 -4.485219164x + x2 = 0 + -1.22324159 Combine like terms: 0 + -1.22324159 = -1.22324159 -4.485219164x + x2 = -1.22324159 The x term is -4.485219164x. Take half its coefficient (-2.242609582). Square it (5.029297737) and add it to both sides. Add '5.029297737' to each side of the equation. -4.485219164x + 5.029297737 + x2 = -1.22324159 + 5.029297737 Reorder the terms: 5.029297737 + -4.485219164x + x2 = -1.22324159 + 5.029297737 Combine like terms: -1.22324159 + 5.029297737 = 3.806056147 5.029297737 + -4.485219164x + x2 = 3.806056147 Factor a perfect square on the left side: (x + -2.242609582)(x + -2.242609582) = 3.806056147 Calculate the square root of the right side: 1.950911619 Break this problem into two subproblems by setting (x + -2.242609582) equal to 1.950911619 and -1.950911619.Subproblem 1
x + -2.242609582 = 1.950911619 Simplifying x + -2.242609582 = 1.950911619 Reorder the terms: -2.242609582 + x = 1.950911619 Solving -2.242609582 + x = 1.950911619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.242609582' to each side of the equation. -2.242609582 + 2.242609582 + x = 1.950911619 + 2.242609582 Combine like terms: -2.242609582 + 2.242609582 = 0.000000000 0.000000000 + x = 1.950911619 + 2.242609582 x = 1.950911619 + 2.242609582 Combine like terms: 1.950911619 + 2.242609582 = 4.193521201 x = 4.193521201 Simplifying x = 4.193521201Subproblem 2
x + -2.242609582 = -1.950911619 Simplifying x + -2.242609582 = -1.950911619 Reorder the terms: -2.242609582 + x = -1.950911619 Solving -2.242609582 + x = -1.950911619 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.242609582' to each side of the equation. -2.242609582 + 2.242609582 + x = -1.950911619 + 2.242609582 Combine like terms: -2.242609582 + 2.242609582 = 0.000000000 0.000000000 + x = -1.950911619 + 2.242609582 x = -1.950911619 + 2.242609582 Combine like terms: -1.950911619 + 2.242609582 = 0.291697963 x = 0.291697963 Simplifying x = 0.291697963Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.193521201, 0.291697963}
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