4x^2-20x+25=35

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Solution for 4x^2-20x+25=35 equation:


Simplifying
4x2 + -20x + 25 = 35

Reorder the terms:
25 + -20x + 4x2 = 35

Solving
25 + -20x + 4x2 = 35

Solving for variable 'x'.

Reorder the terms:
25 + -35 + -20x + 4x2 = 35 + -35

Combine like terms: 25 + -35 = -10
-10 + -20x + 4x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-10 + -20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -10x + 2x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-5 + -10x + 2x2)' equal to zero and attempt to solve: Simplifying -5 + -10x + 2x2 = 0 Solving -5 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5x + x2 = 0 + 2.5 -5x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5x + x2 = 2.5 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 = 2.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5x + x2 = 8.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (x + -2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

x + -2.5 = 2.958039892 Simplifying x + -2.5 = 2.958039892 Reorder the terms: -2.5 + x = 2.958039892 Solving -2.5 + x = 2.958039892 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 = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 2.958039892 + 2.5 x = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 x = 5.458039892 Simplifying x = 5.458039892

Subproblem 2

x + -2.5 = -2.958039892 Simplifying x + -2.5 = -2.958039892 Reorder the terms: -2.5 + x = -2.958039892 Solving -2.5 + x = -2.958039892 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 = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -2.958039892 + 2.5 x = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 x = -0.458039892 Simplifying x = -0.458039892

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.458039892, -0.458039892}

Solution

x = {5.458039892, -0.458039892}

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