5x^2-20x+20=x^2

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Solution for 5x^2-20x+20=x^2 equation:


Simplifying
5x2 + -20x + 20 = x2

Reorder the terms:
20 + -20x + 5x2 = x2

Solving
20 + -20x + 5x2 = x2

Solving for variable 'x'.

Combine like terms: 5x2 + -1x2 = 4x2
20 + -20x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + -5x + x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(5 + -5x + x2)' equal to zero and attempt to solve: Simplifying 5 + -5x + x2 = 0 Solving 5 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -5x + x2 = 0 + -5 -5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -5x + x2 = -5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -5 + 6.25 Combine like terms: -5 + 6.25 = 1.25 6.25 + -5x + x2 = 1.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (x + -2.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -2.5 = 1.118033989 Simplifying x + -2.5 = 1.118033989 Reorder the terms: -2.5 + x = 1.118033989 Solving -2.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.118033989 + 2.5 x = 1.118033989 + 2.5 Combine like terms: 1.118033989 + 2.5 = 3.618033989 x = 3.618033989 Simplifying x = 3.618033989

Subproblem 2

x + -2.5 = -1.118033989 Simplifying x + -2.5 = -1.118033989 Reorder the terms: -2.5 + x = -1.118033989 Solving -2.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.118033989 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.118033989 + 2.5 x = -1.118033989 + 2.5 Combine like terms: -1.118033989 + 2.5 = 1.381966011 x = 1.381966011 Simplifying x = 1.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.618033989, 1.381966011}

Solution

x = {3.618033989, 1.381966011}

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