16x^2-16x=25

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Solution for 16x^2-16x=25 equation:


Simplifying
16x2 + -16x = 25

Reorder the terms:
-16x + 16x2 = 25

Solving
-16x + 16x2 = 25

Solving for variable 'x'.

Reorder the terms:
-25 + -16x + 16x2 = 25 + -25

Combine like terms: 25 + -25 = 0
-25 + -16x + 16x2 = 0

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

Divide each side by '16'.
-1.5625 + -1x + x2 = 0

Move the constant term to the right:

Add '1.5625' to each side of the equation.
-1.5625 + -1x + 1.5625 + x2 = 0 + 1.5625

Reorder the terms:
-1.5625 + 1.5625 + -1x + x2 = 0 + 1.5625

Combine like terms: -1.5625 + 1.5625 = 0.0000
0.0000 + -1x + x2 = 0 + 1.5625
-1x + x2 = 0 + 1.5625

Combine like terms: 0 + 1.5625 = 1.5625
-1x + x2 = 1.5625

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1.5625 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.5625 + 0.25

Combine like terms: 1.5625 + 0.25 = 1.8125
0.25 + -1x + x2 = 1.8125

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.8125

Calculate the square root of the right side: 1.346291202

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.346291202 and -1.346291202.

Subproblem 1

x + -0.5 = 1.346291202 Simplifying x + -0.5 = 1.346291202 Reorder the terms: -0.5 + x = 1.346291202 Solving -0.5 + x = 1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.346291202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.346291202 + 0.5 x = 1.346291202 + 0.5 Combine like terms: 1.346291202 + 0.5 = 1.846291202 x = 1.846291202 Simplifying x = 1.846291202

Subproblem 2

x + -0.5 = -1.346291202 Simplifying x + -0.5 = -1.346291202 Reorder the terms: -0.5 + x = -1.346291202 Solving -0.5 + x = -1.346291202 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.346291202 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.346291202 + 0.5 x = -1.346291202 + 0.5 Combine like terms: -1.346291202 + 0.5 = -0.846291202 x = -0.846291202 Simplifying x = -0.846291202

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.846291202, -0.846291202}

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