5x^2-25x=20

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Solution for 5x^2-25x=20 equation:


Simplifying
5x2 + -25x = 20

Reorder the terms:
-25x + 5x2 = 20

Solving
-25x + 5x2 = 20

Solving for variable 'x'.

Reorder the terms:
-20 + -25x + 5x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -25x + 5x2 = 0

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

Ignore the factor 5.

Subproblem 1

Set the factor '(-4 + -5x + x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + x2 = 0 Solving -4 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -5x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -5x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5x + x2 = 0 + 4 -5x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -5x + x2 = 4 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 = 4 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4 + 6.25 Combine like terms: 4 + 6.25 = 10.25 6.25 + -5x + x2 = 10.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -2.5) equal to 3.201562119 and -3.201562119.

Subproblem 1

x + -2.5 = 3.201562119 Simplifying x + -2.5 = 3.201562119 Reorder the terms: -2.5 + x = 3.201562119 Solving -2.5 + x = 3.201562119 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 = 3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.201562119 + 2.5 x = 3.201562119 + 2.5 Combine like terms: 3.201562119 + 2.5 = 5.701562119 x = 5.701562119 Simplifying x = 5.701562119

Subproblem 2

x + -2.5 = -3.201562119 Simplifying x + -2.5 = -3.201562119 Reorder the terms: -2.5 + x = -3.201562119 Solving -2.5 + x = -3.201562119 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 = -3.201562119 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.201562119 + 2.5 x = -3.201562119 + 2.5 Combine like terms: -3.201562119 + 2.5 = -0.701562119 x = -0.701562119 Simplifying x = -0.701562119

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.701562119, -0.701562119}

Solution

x = {5.701562119, -0.701562119}

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