15+2x+4x^2=192

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Solution for 15+2x+4x^2=192 equation:


Simplifying
15 + 2x + 4x2 = 192

Solving
15 + 2x + 4x2 = 192

Solving for variable 'x'.

Reorder the terms:
15 + -192 + 2x + 4x2 = 192 + -192

Combine like terms: 15 + -192 = -177
-177 + 2x + 4x2 = 192 + -192

Combine like terms: 192 + -192 = 0
-177 + 2x + 4x2 = 0

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

Divide each side by '4'.
-44.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '44.25' to each side of the equation.
-44.25 + 0.5x + 44.25 + x2 = 0 + 44.25

Reorder the terms:
-44.25 + 44.25 + 0.5x + x2 = 0 + 44.25

Combine like terms: -44.25 + 44.25 = 0.00
0.00 + 0.5x + x2 = 0 + 44.25
0.5x + x2 = 0 + 44.25

Combine like terms: 0 + 44.25 = 44.25
0.5x + x2 = 44.25

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 44.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 44.25 + 0.0625

Combine like terms: 44.25 + 0.0625 = 44.3125
0.0625 + 0.5x + x2 = 44.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 44.3125

Calculate the square root of the right side: 6.656763478

Break this problem into two subproblems by setting 
(x + 0.25) equal to 6.656763478 and -6.656763478.

Subproblem 1

x + 0.25 = 6.656763478 Simplifying x + 0.25 = 6.656763478 Reorder the terms: 0.25 + x = 6.656763478 Solving 0.25 + x = 6.656763478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 6.656763478 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 6.656763478 + -0.25 x = 6.656763478 + -0.25 Combine like terms: 6.656763478 + -0.25 = 6.406763478 x = 6.406763478 Simplifying x = 6.406763478

Subproblem 2

x + 0.25 = -6.656763478 Simplifying x + 0.25 = -6.656763478 Reorder the terms: 0.25 + x = -6.656763478 Solving 0.25 + x = -6.656763478 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -6.656763478 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -6.656763478 + -0.25 x = -6.656763478 + -0.25 Combine like terms: -6.656763478 + -0.25 = -6.906763478 x = -6.906763478 Simplifying x = -6.906763478

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.406763478, -6.906763478}

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