49x^2+70x+25=48

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Solution for 49x^2+70x+25=48 equation:


Simplifying
49x2 + 70x + 25 = 48

Reorder the terms:
25 + 70x + 49x2 = 48

Solving
25 + 70x + 49x2 = 48

Solving for variable 'x'.

Reorder the terms:
25 + -48 + 70x + 49x2 = 48 + -48

Combine like terms: 25 + -48 = -23
-23 + 70x + 49x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-23 + 70x + 49x2 = 0

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

Divide each side by '49'.
-0.4693877551 + 1.428571429x + x2 = 0

Move the constant term to the right:

Add '0.4693877551' to each side of the equation.
-0.4693877551 + 1.428571429x + 0.4693877551 + x2 = 0 + 0.4693877551

Reorder the terms:
-0.4693877551 + 0.4693877551 + 1.428571429x + x2 = 0 + 0.4693877551

Combine like terms: -0.4693877551 + 0.4693877551 = 0.0000000000
0.0000000000 + 1.428571429x + x2 = 0 + 0.4693877551
1.428571429x + x2 = 0 + 0.4693877551

Combine like terms: 0 + 0.4693877551 = 0.4693877551
1.428571429x + x2 = 0.4693877551

The x term is 1.428571429x.  Take half its coefficient (0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
1.428571429x + 0.5102040819 + x2 = 0.4693877551 + 0.5102040819

Reorder the terms:
0.5102040819 + 1.428571429x + x2 = 0.4693877551 + 0.5102040819

Combine like terms: 0.4693877551 + 0.5102040819 = 0.979591837
0.5102040819 + 1.428571429x + x2 = 0.979591837

Factor a perfect square on the left side:
(x + 0.7142857145)(x + 0.7142857145) = 0.979591837

Calculate the square root of the right side: 0.989743319

Break this problem into two subproblems by setting 
(x + 0.7142857145) equal to 0.989743319 and -0.989743319.

Subproblem 1

x + 0.7142857145 = 0.989743319 Simplifying x + 0.7142857145 = 0.989743319 Reorder the terms: 0.7142857145 + x = 0.989743319 Solving 0.7142857145 + x = 0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = 0.989743319 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = 0.989743319 + -0.7142857145 x = 0.989743319 + -0.7142857145 Combine like terms: 0.989743319 + -0.7142857145 = 0.2754576045 x = 0.2754576045 Simplifying x = 0.2754576045

Subproblem 2

x + 0.7142857145 = -0.989743319 Simplifying x + 0.7142857145 = -0.989743319 Reorder the terms: 0.7142857145 + x = -0.989743319 Solving 0.7142857145 + x = -0.989743319 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7142857145' to each side of the equation. 0.7142857145 + -0.7142857145 + x = -0.989743319 + -0.7142857145 Combine like terms: 0.7142857145 + -0.7142857145 = 0.0000000000 0.0000000000 + x = -0.989743319 + -0.7142857145 x = -0.989743319 + -0.7142857145 Combine like terms: -0.989743319 + -0.7142857145 = -1.7040290335 x = -1.7040290335 Simplifying x = -1.7040290335

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2754576045, -1.7040290335}

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