2x^2-8x=400

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Solution for 2x^2-8x=400 equation:


Simplifying
2x2 + -8x = 400

Reorder the terms:
-8x + 2x2 = 400

Solving
-8x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -8x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-200 + -4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-200 + -4x + x2)' equal to zero and attempt to solve: Simplifying -200 + -4x + x2 = 0 Solving -200 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -4x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -4x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -4x + x2 = 0 + 200 -4x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -4x + x2 = 200 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 200 + 4 Reorder the terms: 4 + -4x + x2 = 200 + 4 Combine like terms: 200 + 4 = 204 4 + -4x + x2 = 204 Factor a perfect square on the left side: (x + -2)(x + -2) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (x + -2) equal to 14.282856857 and -14.282856857.

Subproblem 1

x + -2 = 14.282856857 Simplifying x + -2 = 14.282856857 Reorder the terms: -2 + x = 14.282856857 Solving -2 + x = 14.282856857 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 + x = 14.282856857 + 2 Combine like terms: -2 + 2 = 0 0 + x = 14.282856857 + 2 x = 14.282856857 + 2 Combine like terms: 14.282856857 + 2 = 16.282856857 x = 16.282856857 Simplifying x = 16.282856857

Subproblem 2

x + -2 = -14.282856857 Simplifying x + -2 = -14.282856857 Reorder the terms: -2 + x = -14.282856857 Solving -2 + x = -14.282856857 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 + x = -14.282856857 + 2 Combine like terms: -2 + 2 = 0 0 + x = -14.282856857 + 2 x = -14.282856857 + 2 Combine like terms: -14.282856857 + 2 = -12.282856857 x = -12.282856857 Simplifying x = -12.282856857

Solution

The solution to the problem is based on the solutions from the subproblems. x = {16.282856857, -12.282856857}

Solution

x = {16.282856857, -12.282856857}

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