4x^2-80x=400

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Solution for 4x^2-80x=400 equation:


Simplifying
4x2 + -80x = 400

Reorder the terms:
-80x + 4x2 = 400

Solving
-80x + 4x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + -80x + 4x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + -80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-100 + -20x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-100 + -20x + x2)' equal to zero and attempt to solve: Simplifying -100 + -20x + x2 = 0 Solving -100 + -20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -20x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -20x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -20x + x2 = 0 + 100 -20x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -20x + x2 = 100 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 100 + 100 Reorder the terms: 100 + -20x + x2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + -20x + x2 = 200 Factor a perfect square on the left side: (x + -10)(x + -10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (x + -10) equal to 14.142135624 and -14.142135624.

Subproblem 1

x + -10 = 14.142135624 Simplifying x + -10 = 14.142135624 Reorder the terms: -10 + x = 14.142135624 Solving -10 + x = 14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + x = 14.142135624 + 10 x = 14.142135624 + 10 Combine like terms: 14.142135624 + 10 = 24.142135624 x = 24.142135624 Simplifying x = 24.142135624

Subproblem 2

x + -10 = -14.142135624 Simplifying x + -10 = -14.142135624 Reorder the terms: -10 + x = -14.142135624 Solving -10 + x = -14.142135624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -14.142135624 + 10 Combine like terms: -10 + 10 = 0 0 + x = -14.142135624 + 10 x = -14.142135624 + 10 Combine like terms: -14.142135624 + 10 = -4.142135624 x = -4.142135624 Simplifying x = -4.142135624

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.142135624, -4.142135624}

Solution

x = {24.142135624, -4.142135624}

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