(2x^2)-840x+26352=0

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Solution for (2x^2)-840x+26352=0 equation:


Simplifying
(2x2) + -840x + 26352 = 0

Reorder the terms:
26352 + -840x + (2x2) = 0

Solving
26352 + -840x + (2x2) = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(13176 + -420x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(13176 + -420x + x2)' equal to zero and attempt to solve: Simplifying 13176 + -420x + x2 = 0 Solving 13176 + -420x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-13176' to each side of the equation. 13176 + -420x + -13176 + x2 = 0 + -13176 Reorder the terms: 13176 + -13176 + -420x + x2 = 0 + -13176 Combine like terms: 13176 + -13176 = 0 0 + -420x + x2 = 0 + -13176 -420x + x2 = 0 + -13176 Combine like terms: 0 + -13176 = -13176 -420x + x2 = -13176 The x term is -420x. Take half its coefficient (-210). Square it (44100) and add it to both sides. Add '44100' to each side of the equation. -420x + 44100 + x2 = -13176 + 44100 Reorder the terms: 44100 + -420x + x2 = -13176 + 44100 Combine like terms: -13176 + 44100 = 30924 44100 + -420x + x2 = 30924 Factor a perfect square on the left side: (x + -210)(x + -210) = 30924 Calculate the square root of the right side: 175.852210677 Break this problem into two subproblems by setting (x + -210) equal to 175.852210677 and -175.852210677.

Subproblem 1

x + -210 = 175.852210677 Simplifying x + -210 = 175.852210677 Reorder the terms: -210 + x = 175.852210677 Solving -210 + x = 175.852210677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '210' to each side of the equation. -210 + 210 + x = 175.852210677 + 210 Combine like terms: -210 + 210 = 0 0 + x = 175.852210677 + 210 x = 175.852210677 + 210 Combine like terms: 175.852210677 + 210 = 385.852210677 x = 385.852210677 Simplifying x = 385.852210677

Subproblem 2

x + -210 = -175.852210677 Simplifying x + -210 = -175.852210677 Reorder the terms: -210 + x = -175.852210677 Solving -210 + x = -175.852210677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '210' to each side of the equation. -210 + 210 + x = -175.852210677 + 210 Combine like terms: -210 + 210 = 0 0 + x = -175.852210677 + 210 x = -175.852210677 + 210 Combine like terms: -175.852210677 + 210 = 34.147789323 x = 34.147789323 Simplifying x = 34.147789323

Solution

The solution to the problem is based on the solutions from the subproblems. x = {385.852210677, 34.147789323}

Solution

x = {385.852210677, 34.147789323}

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