10000x^4-110000000x^2+10000000000=0

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Solution for 10000x^4-110000000x^2+10000000000=0 equation:


Simplifying
10000x4 + -110000000x2 + 10000000000 = 0

Reorder the terms:
10000000000 + -110000000x2 + 10000x4 = 0

Solving
10000000000 + -110000000x2 + 10000x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10000'.
10000(1000000 + -11000x2 + x4) = 0

Ignore the factor 10000.

Subproblem 1

Set the factor '(1000000 + -11000x2 + x4)' equal to zero and attempt to solve: Simplifying 1000000 + -11000x2 + x4 = 0 Solving 1000000 + -11000x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-1000000' to each side of the equation. 1000000 + -11000x2 + -1000000 + x4 = 0 + -1000000 Reorder the terms: 1000000 + -1000000 + -11000x2 + x4 = 0 + -1000000 Combine like terms: 1000000 + -1000000 = 0 0 + -11000x2 + x4 = 0 + -1000000 -11000x2 + x4 = 0 + -1000000 Combine like terms: 0 + -1000000 = -1000000 -11000x2 + x4 = -1000000 The x term is -11000x2. Take half its coefficient (-5500). Square it (30250000) and add it to both sides. Add '30250000' to each side of the equation. -11000x2 + 30250000 + x4 = -1000000 + 30250000 Reorder the terms: 30250000 + -11000x2 + x4 = -1000000 + 30250000 Combine like terms: -1000000 + 30250000 = 29250000 30250000 + -11000x2 + x4 = 29250000 Factor a perfect square on the left side: (x2 + -5500)(x2 + -5500) = 29250000 Calculate the square root of the right side: 5408.326913196 Break this problem into two subproblems by setting (x2 + -5500) equal to 5408.326913196 and -5408.326913196.

Subproblem 1

x2 + -5500 = 5408.326913196 Simplifying x2 + -5500 = 5408.326913196 Reorder the terms: -5500 + x2 = 5408.326913196 Solving -5500 + x2 = 5408.326913196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5500' to each side of the equation. -5500 + 5500 + x2 = 5408.326913196 + 5500 Combine like terms: -5500 + 5500 = 0 0 + x2 = 5408.326913196 + 5500 x2 = 5408.326913196 + 5500 Combine like terms: 5408.326913196 + 5500 = 10908.326913196 x2 = 10908.326913196 Simplifying x2 = 10908.326913196 Take the square root of each side: x = {-104.442936157, 104.442936157}

Subproblem 2

x2 + -5500 = -5408.326913196 Simplifying x2 + -5500 = -5408.326913196 Reorder the terms: -5500 + x2 = -5408.326913196 Solving -5500 + x2 = -5408.326913196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5500' to each side of the equation. -5500 + 5500 + x2 = -5408.326913196 + 5500 Combine like terms: -5500 + 5500 = 0 0 + x2 = -5408.326913196 + 5500 x2 = -5408.326913196 + 5500 Combine like terms: -5408.326913196 + 5500 = 91.673086804 x2 = 91.673086804 Simplifying x2 = 91.673086804 Take the square root of each side: x = {-9.574606352, 9.574606352}

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-104.442936157, 104.442936157, -9.574606352, 9.574606352}

Solution

x = {-104.442936157, 104.442936157, -9.574606352, 9.574606352}

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