.50(x)+13=14(x)1.25(x)

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Solution for .50(x)+13=14(x)1.25(x) equation:


Simplifying
0.50(x) + 13 = 14(x) * 1.25(x)

Reorder the terms:
13 + 0.50x = 14(x) * 1.25(x)

Reorder the terms for easier multiplication:
13 + 0.50x = 14 * 1.25x * x

Multiply 14 * 1.25
13 + 0.50x = 17.5x * x

Multiply x * x
13 + 0.50x = 17.5x2

Solving
13 + 0.50x = 17.5x2

Solving for variable 'x'.

Combine like terms: 17.5x2 + -17.5x2 = 0.0
13 + 0.50x + -17.5x2 = 0.0

Begin completing the square.  Divide all terms by
-17.5 the coefficient of the squared term: 

Divide each side by '-17.5'.
-0.7428571429 + -0.02857142857x + x2 = 0

Move the constant term to the right:

Add '0.7428571429' to each side of the equation.
-0.7428571429 + -0.02857142857x + 0.7428571429 + x2 = 0 + 0.7428571429

Reorder the terms:
-0.7428571429 + 0.7428571429 + -0.02857142857x + x2 = 0 + 0.7428571429

Combine like terms: -0.7428571429 + 0.7428571429 = 0.0000000000
0.0000000000 + -0.02857142857x + x2 = 0 + 0.7428571429
-0.02857142857x + x2 = 0 + 0.7428571429

Combine like terms: 0 + 0.7428571429 = 0.7428571429
-0.02857142857x + x2 = 0.7428571429

The x term is -0.02857142857x.  Take half its coefficient (-0.01428571429).
Square it (0.0002040816328) and add it to both sides.

Add '0.0002040816328' to each side of the equation.
-0.02857142857x + 0.0002040816328 + x2 = 0.7428571429 + 0.0002040816328

Reorder the terms:
0.0002040816328 + -0.02857142857x + x2 = 0.7428571429 + 0.0002040816328

Combine like terms: 0.7428571429 + 0.0002040816328 = 0.7430612245328
0.0002040816328 + -0.02857142857x + x2 = 0.7430612245328

Factor a perfect square on the left side:
(x + -0.01428571429)(x + -0.01428571429) = 0.7430612245328

Calculate the square root of the right side: 0.862009991

Break this problem into two subproblems by setting 
(x + -0.01428571429) equal to 0.862009991 and -0.862009991.

Subproblem 1

x + -0.01428571429 = 0.862009991 Simplifying x + -0.01428571429 = 0.862009991 Reorder the terms: -0.01428571429 + x = 0.862009991 Solving -0.01428571429 + x = 0.862009991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + x = 0.862009991 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + x = 0.862009991 + 0.01428571429 x = 0.862009991 + 0.01428571429 Combine like terms: 0.862009991 + 0.01428571429 = 0.87629570529 x = 0.87629570529 Simplifying x = 0.87629570529

Subproblem 2

x + -0.01428571429 = -0.862009991 Simplifying x + -0.01428571429 = -0.862009991 Reorder the terms: -0.01428571429 + x = -0.862009991 Solving -0.01428571429 + x = -0.862009991 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01428571429' to each side of the equation. -0.01428571429 + 0.01428571429 + x = -0.862009991 + 0.01428571429 Combine like terms: -0.01428571429 + 0.01428571429 = 0.00000000000 0.00000000000 + x = -0.862009991 + 0.01428571429 x = -0.862009991 + 0.01428571429 Combine like terms: -0.862009991 + 0.01428571429 = -0.84772427671 x = -0.84772427671 Simplifying x = -0.84772427671

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.87629570529, -0.84772427671}

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