0=-16x^2+48x+15

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Solution for 0=-16x^2+48x+15 equation:


Simplifying
0 = -16x2 + 48x + 15

Reorder the terms:
0 = 15 + 48x + -16x2

Solving
0 = 15 + 48x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -15 = -15
-15 + -48x + 16x2 = 15 + 48x + -16x2 + -15 + -48x + 16x2

Reorder the terms:
-15 + -48x + 16x2 = 15 + -15 + 48x + -48x + -16x2 + 16x2

Combine like terms: 15 + -15 = 0
-15 + -48x + 16x2 = 0 + 48x + -48x + -16x2 + 16x2
-15 + -48x + 16x2 = 48x + -48x + -16x2 + 16x2

Combine like terms: 48x + -48x = 0
-15 + -48x + 16x2 = 0 + -16x2 + 16x2
-15 + -48x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-15 + -48x + 16x2 = 0

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

Divide each side by '16'.
-0.9375 + -3x + x2 = 0

Move the constant term to the right:

Add '0.9375' to each side of the equation.
-0.9375 + -3x + 0.9375 + x2 = 0 + 0.9375

Reorder the terms:
-0.9375 + 0.9375 + -3x + x2 = 0 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + -3x + x2 = 0 + 0.9375
-3x + x2 = 0 + 0.9375

Combine like terms: 0 + 0.9375 = 0.9375
-3x + x2 = 0.9375

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 0.9375 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 0.9375 + 2.25

Combine like terms: 0.9375 + 2.25 = 3.1875
2.25 + -3x + x2 = 3.1875

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 3.1875

Calculate the square root of the right side: 1.785357107

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.785357107 and -1.785357107.

Subproblem 1

x + -1.5 = 1.785357107 Simplifying x + -1.5 = 1.785357107 Reorder the terms: -1.5 + x = 1.785357107 Solving -1.5 + x = 1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.785357107 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.785357107 + 1.5 x = 1.785357107 + 1.5 Combine like terms: 1.785357107 + 1.5 = 3.285357107 x = 3.285357107 Simplifying x = 3.285357107

Subproblem 2

x + -1.5 = -1.785357107 Simplifying x + -1.5 = -1.785357107 Reorder the terms: -1.5 + x = -1.785357107 Solving -1.5 + x = -1.785357107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.785357107 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.785357107 + 1.5 x = -1.785357107 + 1.5 Combine like terms: -1.785357107 + 1.5 = -0.285357107 x = -0.285357107 Simplifying x = -0.285357107

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.285357107, -0.285357107}

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