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Simplifying 3x4 + -24x2 + 16 = 0 Reorder the terms: 16 + -24x2 + 3x4 = 0 Solving 16 + -24x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.333333333 + -8x2 + x4 = 0 Move the constant term to the right: Add '-5.333333333' to each side of the equation. 5.333333333 + -8x2 + -5.333333333 + x4 = 0 + -5.333333333 Reorder the terms: 5.333333333 + -5.333333333 + -8x2 + x4 = 0 + -5.333333333 Combine like terms: 5.333333333 + -5.333333333 = 0.000000000 0.000000000 + -8x2 + x4 = 0 + -5.333333333 -8x2 + x4 = 0 + -5.333333333 Combine like terms: 0 + -5.333333333 = -5.333333333 -8x2 + x4 = -5.333333333 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -5.333333333 + 16 Reorder the terms: 16 + -8x2 + x4 = -5.333333333 + 16 Combine like terms: -5.333333333 + 16 = 10.666666667 16 + -8x2 + x4 = 10.666666667 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x2 + -4) equal to 3.265986324 and -3.265986324.Subproblem 1
x2 + -4 = 3.265986324 Simplifying x2 + -4 = 3.265986324 Reorder the terms: -4 + x2 = 3.265986324 Solving -4 + x2 = 3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = 3.265986324 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = 3.265986324 + 4 x2 = 3.265986324 + 4 Combine like terms: 3.265986324 + 4 = 7.265986324 x2 = 7.265986324 Simplifying x2 = 7.265986324 Take the square root of each side: x = {-2.695549355, 2.695549355}Subproblem 2
x2 + -4 = -3.265986324 Simplifying x2 + -4 = -3.265986324 Reorder the terms: -4 + x2 = -3.265986324 Solving -4 + x2 = -3.265986324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x2 = -3.265986324 + 4 Combine like terms: -4 + 4 = 0 0 + x2 = -3.265986324 + 4 x2 = -3.265986324 + 4 Combine like terms: -3.265986324 + 4 = 0.734013676 x2 = 0.734013676 Simplifying x2 = 0.734013676 Take the square root of each side: x = {-0.856745981, 0.856745981}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.695549355, 2.695549355, -0.856745981, 0.856745981}
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