5x^2-4x=25

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Solution for 5x^2-4x=25 equation:


Simplifying
5x2 + -4x = 25

Reorder the terms:
-4x + 5x2 = 25

Solving
-4x + 5x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + -4x + 5x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -4x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-5 + -0.8x + x2 = 0

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -0.8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -0.8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -0.8x + x2 = 0 + 5
-0.8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-0.8x + x2 = 5

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 5 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 5 + 0.16

Combine like terms: 5 + 0.16 = 5.16
0.16 + -0.8x + x2 = 5.16

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 5.16

Calculate the square root of the right side: 2.271563338

Break this problem into two subproblems by setting 
(x + -0.4) equal to 2.271563338 and -2.271563338.

Subproblem 1

x + -0.4 = 2.271563338 Simplifying x + -0.4 = 2.271563338 Reorder the terms: -0.4 + x = 2.271563338 Solving -0.4 + x = 2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 2.271563338 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 2.271563338 + 0.4 x = 2.271563338 + 0.4 Combine like terms: 2.271563338 + 0.4 = 2.671563338 x = 2.671563338 Simplifying x = 2.671563338

Subproblem 2

x + -0.4 = -2.271563338 Simplifying x + -0.4 = -2.271563338 Reorder the terms: -0.4 + x = -2.271563338 Solving -0.4 + x = -2.271563338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -2.271563338 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -2.271563338 + 0.4 x = -2.271563338 + 0.4 Combine like terms: -2.271563338 + 0.4 = -1.871563338 x = -1.871563338 Simplifying x = -1.871563338

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.671563338, -1.871563338}

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