4x^2+30x+25=

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Solution for 4x^2+30x+25= equation:


Simplifying
4x2 + 30x + 25 = 0

Reorder the terms:
25 + 30x + 4x2 = 0

Solving
25 + 30x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
6.25 + 7.5x + x2 = 0

Move the constant term to the right:

Add '-6.25' to each side of the equation.
6.25 + 7.5x + -6.25 + x2 = 0 + -6.25

Reorder the terms:
6.25 + -6.25 + 7.5x + x2 = 0 + -6.25

Combine like terms: 6.25 + -6.25 = 0.00
0.00 + 7.5x + x2 = 0 + -6.25
7.5x + x2 = 0 + -6.25

Combine like terms: 0 + -6.25 = -6.25
7.5x + x2 = -6.25

The x term is 7.5x.  Take half its coefficient (3.75).
Square it (14.0625) and add it to both sides.

Add '14.0625' to each side of the equation.
7.5x + 14.0625 + x2 = -6.25 + 14.0625

Reorder the terms:
14.0625 + 7.5x + x2 = -6.25 + 14.0625

Combine like terms: -6.25 + 14.0625 = 7.8125
14.0625 + 7.5x + x2 = 7.8125

Factor a perfect square on the left side:
(x + 3.75)(x + 3.75) = 7.8125

Calculate the square root of the right side: 2.795084972

Break this problem into two subproblems by setting 
(x + 3.75) equal to 2.795084972 and -2.795084972.

Subproblem 1

x + 3.75 = 2.795084972 Simplifying x + 3.75 = 2.795084972 Reorder the terms: 3.75 + x = 2.795084972 Solving 3.75 + x = 2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 2.795084972 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 2.795084972 + -3.75 x = 2.795084972 + -3.75 Combine like terms: 2.795084972 + -3.75 = -0.954915028 x = -0.954915028 Simplifying x = -0.954915028

Subproblem 2

x + 3.75 = -2.795084972 Simplifying x + 3.75 = -2.795084972 Reorder the terms: 3.75 + x = -2.795084972 Solving 3.75 + x = -2.795084972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -2.795084972 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -2.795084972 + -3.75 x = -2.795084972 + -3.75 Combine like terms: -2.795084972 + -3.75 = -6.545084972 x = -6.545084972 Simplifying x = -6.545084972

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.954915028, -6.545084972}

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