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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 = 6.252539327 5.029297737 + 4.485219164x + x2 = 6.252539327 Factor a perfect square on the left side: (x + 2.242609582)(x + 2.242609582) = 6.252539327 Calculate the square root of the right side: 2.500507814 Break this problem into two subproblems by setting (x + 2.242609582) equal to 2.500507814 and -2.500507814.Subproblem 1
x + 2.242609582 = 2.500507814 Simplifying x + 2.242609582 = 2.500507814 Reorder the terms: 2.242609582 + x = 2.500507814 Solving 2.242609582 + x = 2.500507814 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 = 2.500507814 + -2.242609582 Combine like terms: 2.242609582 + -2.242609582 = 0.000000000 0.000000000 + x = 2.500507814 + -2.242609582 x = 2.500507814 + -2.242609582 Combine like terms: 2.500507814 + -2.242609582 = 0.257898232 x = 0.257898232 Simplifying x = 0.257898232Subproblem 2
x + 2.242609582 = -2.500507814 Simplifying x + 2.242609582 = -2.500507814 Reorder the terms: 2.242609582 + x = -2.500507814 Solving 2.242609582 + x = -2.500507814 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 = -2.500507814 + -2.242609582 Combine like terms: 2.242609582 + -2.242609582 = 0.000000000 0.000000000 + x = -2.500507814 + -2.242609582 x = -2.500507814 + -2.242609582 Combine like terms: -2.500507814 + -2.242609582 = -4.743117396 x = -4.743117396 Simplifying x = -4.743117396Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.257898232, -4.743117396}
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