2x^2+4x=400

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Solution for 2x^2+4x=400 equation:


Simplifying
2x2 + 4x = 400

Reorder the terms:
4x + 2x2 = 400

Solving
4x + 2x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 4x + 2x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 4x + 2x2 = 0

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

Ignore the factor 2.

Subproblem 1

Set the factor '(-200 + 2x + x2)' equal to zero and attempt to solve: Simplifying -200 + 2x + x2 = 0 Solving -200 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 2x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 2x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 2x + x2 = 0 + 200 2x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 2x + x2 = 200 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 200 + 1 Reorder the terms: 1 + 2x + x2 = 200 + 1 Combine like terms: 200 + 1 = 201 1 + 2x + x2 = 201 Factor a perfect square on the left side: (x + 1)(x + 1) = 201 Calculate the square root of the right side: 14.177446879 Break this problem into two subproblems by setting (x + 1) equal to 14.177446879 and -14.177446879.

Subproblem 1

x + 1 = 14.177446879 Simplifying x + 1 = 14.177446879 Reorder the terms: 1 + x = 14.177446879 Solving 1 + x = 14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + x = 14.177446879 + -1 x = 14.177446879 + -1 Combine like terms: 14.177446879 + -1 = 13.177446879 x = 13.177446879 Simplifying x = 13.177446879

Subproblem 2

x + 1 = -14.177446879 Simplifying x + 1 = -14.177446879 Reorder the terms: 1 + x = -14.177446879 Solving 1 + x = -14.177446879 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -14.177446879 + -1 Combine like terms: 1 + -1 = 0 0 + x = -14.177446879 + -1 x = -14.177446879 + -1 Combine like terms: -14.177446879 + -1 = -15.177446879 x = -15.177446879 Simplifying x = -15.177446879

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.177446879, -15.177446879}

Solution

x = {13.177446879, -15.177446879}

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