4x^2+28x+15=0

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Solution for 4x^2+28x+15=0 equation:


Simplifying
4x2 + 28x + 15 = 0

Reorder the terms:
15 + 28x + 4x2 = 0

Solving
15 + 28x + 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'.
3.75 + 7x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 7x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 7x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 7x + x2 = 0 + -3.75
7x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
7x + x2 = -3.75

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -3.75 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -3.75 + 12.25

Combine like terms: -3.75 + 12.25 = 8.5
12.25 + 7x + x2 = 8.5

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 8.5

Calculate the square root of the right side: 2.915475947

Break this problem into two subproblems by setting 
(x + 3.5) equal to 2.915475947 and -2.915475947.

Subproblem 1

x + 3.5 = 2.915475947 Simplifying x + 3.5 = 2.915475947 Reorder the terms: 3.5 + x = 2.915475947 Solving 3.5 + x = 2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 2.915475947 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 2.915475947 + -3.5 x = 2.915475947 + -3.5 Combine like terms: 2.915475947 + -3.5 = -0.584524053 x = -0.584524053 Simplifying x = -0.584524053

Subproblem 2

x + 3.5 = -2.915475947 Simplifying x + 3.5 = -2.915475947 Reorder the terms: 3.5 + x = -2.915475947 Solving 3.5 + x = -2.915475947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -2.915475947 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -2.915475947 + -3.5 x = -2.915475947 + -3.5 Combine like terms: -2.915475947 + -3.5 = -6.415475947 x = -6.415475947 Simplifying x = -6.415475947

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.584524053, -6.415475947}

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