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Simplifying x4 + -3136x2 + 3136 = 0 Reorder the terms: 3136 + -3136x2 + x4 = 0 Solving 3136 + -3136x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3136' to each side of the equation. 3136 + -3136x2 + -3136 + x4 = 0 + -3136 Reorder the terms: 3136 + -3136 + -3136x2 + x4 = 0 + -3136 Combine like terms: 3136 + -3136 = 0 0 + -3136x2 + x4 = 0 + -3136 -3136x2 + x4 = 0 + -3136 Combine like terms: 0 + -3136 = -3136 -3136x2 + x4 = -3136 The x term is -3136x2. Take half its coefficient (-1568). Square it (2458624) and add it to both sides. Add '2458624' to each side of the equation. -3136x2 + 2458624 + x4 = -3136 + 2458624 Reorder the terms: 2458624 + -3136x2 + x4 = -3136 + 2458624 Combine like terms: -3136 + 2458624 = 2455488 2458624 + -3136x2 + x4 = 2455488 Factor a perfect square on the left side: (x2 + -1568)(x2 + -1568) = 2455488 Calculate the square root of the right side: 1566.999680919 Break this problem into two subproblems by setting (x2 + -1568) equal to 1566.999680919 and -1566.999680919.Subproblem 1
x2 + -1568 = 1566.999680919 Simplifying x2 + -1568 = 1566.999680919 Reorder the terms: -1568 + x2 = 1566.999680919 Solving -1568 + x2 = 1566.999680919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1568' to each side of the equation. -1568 + 1568 + x2 = 1566.999680919 + 1568 Combine like terms: -1568 + 1568 = 0 0 + x2 = 1566.999680919 + 1568 x2 = 1566.999680919 + 1568 Combine like terms: 1566.999680919 + 1568 = 3134.999680919 x2 = 3134.999680919 Simplifying x2 = 3134.999680919 Take the square root of each side: x = {-55.991067867, 55.991067867}Subproblem 2
x2 + -1568 = -1566.999680919 Simplifying x2 + -1568 = -1566.999680919 Reorder the terms: -1568 + x2 = -1566.999680919 Solving -1568 + x2 = -1566.999680919 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1568' to each side of the equation. -1568 + 1568 + x2 = -1566.999680919 + 1568 Combine like terms: -1568 + 1568 = 0 0 + x2 = -1566.999680919 + 1568 x2 = -1566.999680919 + 1568 Combine like terms: -1566.999680919 + 1568 = 1.000319081 x2 = 1.000319081 Simplifying x2 = 1.000319081 Take the square root of each side: x = {-1.000159528, 1.000159528}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-55.991067867, 55.991067867, -1.000159528, 1.000159528}
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