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Simplifying 49x4 + -18x2 + 1 = 0 Reorder the terms: 1 + -18x2 + 49x4 = 0 Solving 1 + -18x2 + 49x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 49 the coefficient of the squared term: Divide each side by '49'. 0.02040816327 + -0.3673469388x2 + x4 = 0 Move the constant term to the right: Add '-0.02040816327' to each side of the equation. 0.02040816327 + -0.3673469388x2 + -0.02040816327 + x4 = 0 + -0.02040816327 Reorder the terms: 0.02040816327 + -0.02040816327 + -0.3673469388x2 + x4 = 0 + -0.02040816327 Combine like terms: 0.02040816327 + -0.02040816327 = 0.00000000000 0.00000000000 + -0.3673469388x2 + x4 = 0 + -0.02040816327 -0.3673469388x2 + x4 = 0 + -0.02040816327 Combine like terms: 0 + -0.02040816327 = -0.02040816327 -0.3673469388x2 + x4 = -0.02040816327 The x term is -0.3673469388x2. Take half its coefficient (-0.1836734694). Square it (0.03373594336) and add it to both sides. Add '0.03373594336' to each side of the equation. -0.3673469388x2 + 0.03373594336 + x4 = -0.02040816327 + 0.03373594336 Reorder the terms: 0.03373594336 + -0.3673469388x2 + x4 = -0.02040816327 + 0.03373594336 Combine like terms: -0.02040816327 + 0.03373594336 = 0.01332778009 0.03373594336 + -0.3673469388x2 + x4 = 0.01332778009 Factor a perfect square on the left side: (x2 + -0.1836734694)(x2 + -0.1836734694) = 0.01332778009 Calculate the square root of the right side: 0.115446005 Break this problem into two subproblems by setting (x2 + -0.1836734694) equal to 0.115446005 and -0.115446005.Subproblem 1
x2 + -0.1836734694 = 0.115446005 Simplifying x2 + -0.1836734694 = 0.115446005 Reorder the terms: -0.1836734694 + x2 = 0.115446005 Solving -0.1836734694 + x2 = 0.115446005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1836734694' to each side of the equation. -0.1836734694 + 0.1836734694 + x2 = 0.115446005 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + x2 = 0.115446005 + 0.1836734694 x2 = 0.115446005 + 0.1836734694 Combine like terms: 0.115446005 + 0.1836734694 = 0.2991194744 x2 = 0.2991194744 Simplifying x2 = 0.2991194744 Take the square root of each side: x = {-0.546918161, 0.546918161}Subproblem 2
x2 + -0.1836734694 = -0.115446005 Simplifying x2 + -0.1836734694 = -0.115446005 Reorder the terms: -0.1836734694 + x2 = -0.115446005 Solving -0.1836734694 + x2 = -0.115446005 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1836734694' to each side of the equation. -0.1836734694 + 0.1836734694 + x2 = -0.115446005 + 0.1836734694 Combine like terms: -0.1836734694 + 0.1836734694 = 0.0000000000 0.0000000000 + x2 = -0.115446005 + 0.1836734694 x2 = -0.115446005 + 0.1836734694 Combine like terms: -0.115446005 + 0.1836734694 = 0.0682274644 x2 = 0.0682274644 Simplifying x2 = 0.0682274644 Take the square root of each side: x = {-0.261203875, 0.261203875}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.546918161, 0.546918161, -0.261203875, 0.261203875}
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