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Simplifying 3x4 + -12x2 + 5 = 0 Reorder the terms: 5 + -12x2 + 3x4 = 0 Solving 5 + -12x2 + 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'. 1.666666667 + -4x2 + x4 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -4x2 + -1.666666667 + x4 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -4x2 + x4 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -4x2 + x4 = 0 + -1.666666667 -4x2 + x4 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -4x2 + x4 = -1.666666667 The x term is -4x2. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x2 + 4 + x4 = -1.666666667 + 4 Reorder the terms: 4 + -4x2 + x4 = -1.666666667 + 4 Combine like terms: -1.666666667 + 4 = 2.333333333 4 + -4x2 + x4 = 2.333333333 Factor a perfect square on the left side: (x2 + -2)(x2 + -2) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x2 + -2) equal to 1.527525232 and -1.527525232.Subproblem 1
x2 + -2 = 1.527525232 Simplifying x2 + -2 = 1.527525232 Reorder the terms: -2 + x2 = 1.527525232 Solving -2 + x2 = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = 1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = 1.527525232 + 2 x2 = 1.527525232 + 2 Combine like terms: 1.527525232 + 2 = 3.527525232 x2 = 3.527525232 Simplifying x2 = 3.527525232 Take the square root of each side: x = {-1.878170714, 1.878170714}Subproblem 2
x2 + -2 = -1.527525232 Simplifying x2 + -2 = -1.527525232 Reorder the terms: -2 + x2 = -1.527525232 Solving -2 + x2 = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x2 = -1.527525232 + 2 Combine like terms: -2 + 2 = 0 0 + x2 = -1.527525232 + 2 x2 = -1.527525232 + 2 Combine like terms: -1.527525232 + 2 = 0.472474768 x2 = 0.472474768 Simplifying x2 = 0.472474768 Take the square root of each side: x = {-0.687368, 0.687368}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.878170714, 1.878170714, -0.687368, 0.687368}
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