14x^2+70x+25=48

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Solution for 14x^2+70x+25=48 equation:


Simplifying
14x2 + 70x + 25 = 48

Reorder the terms:
25 + 70x + 14x2 = 48

Solving
25 + 70x + 14x2 = 48

Solving for variable 'x'.

Reorder the terms:
25 + -48 + 70x + 14x2 = 48 + -48

Combine like terms: 25 + -48 = -23
-23 + 70x + 14x2 = 48 + -48

Combine like terms: 48 + -48 = 0
-23 + 70x + 14x2 = 0

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

Divide each side by '14'.
-1.642857143 + 5x + x2 = 0

Move the constant term to the right:

Add '1.642857143' to each side of the equation.
-1.642857143 + 5x + 1.642857143 + x2 = 0 + 1.642857143

Reorder the terms:
-1.642857143 + 1.642857143 + 5x + x2 = 0 + 1.642857143

Combine like terms: -1.642857143 + 1.642857143 = 0.000000000
0.000000000 + 5x + x2 = 0 + 1.642857143
5x + x2 = 0 + 1.642857143

Combine like terms: 0 + 1.642857143 = 1.642857143
5x + x2 = 1.642857143

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 = 1.642857143 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1.642857143 + 6.25

Combine like terms: 1.642857143 + 6.25 = 7.892857143
6.25 + 5x + x2 = 7.892857143

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 7.892857143

Calculate the square root of the right side: 2.80942292

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.80942292 and -2.80942292.

Subproblem 1

x + 2.5 = 2.80942292 Simplifying x + 2.5 = 2.80942292 Reorder the terms: 2.5 + x = 2.80942292 Solving 2.5 + x = 2.80942292 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 = 2.80942292 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.80942292 + -2.5 x = 2.80942292 + -2.5 Combine like terms: 2.80942292 + -2.5 = 0.30942292 x = 0.30942292 Simplifying x = 0.30942292

Subproblem 2

x + 2.5 = -2.80942292 Simplifying x + 2.5 = -2.80942292 Reorder the terms: 2.5 + x = -2.80942292 Solving 2.5 + x = -2.80942292 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 = -2.80942292 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.80942292 + -2.5 x = -2.80942292 + -2.5 Combine like terms: -2.80942292 + -2.5 = -5.30942292 x = -5.30942292 Simplifying x = -5.30942292

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.30942292, -5.30942292}

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