-16x^2+80x-69=0

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Solution for -16x^2+80x-69=0 equation:


Simplifying
-16x2 + 80x + -69 = 0

Reorder the terms:
-69 + 80x + -16x2 = 0

Solving
-69 + 80x + -16x2 = 0

Solving for variable 'x'.

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

Divide each side by '-16'.
4.3125 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.3125' to each side of the equation.
4.3125 + -5x + -4.3125 + x2 = 0 + -4.3125

Reorder the terms:
4.3125 + -4.3125 + -5x + x2 = 0 + -4.3125

Combine like terms: 4.3125 + -4.3125 = 0.0000
0.0000 + -5x + x2 = 0 + -4.3125
-5x + x2 = 0 + -4.3125

Combine like terms: 0 + -4.3125 = -4.3125
-5x + x2 = -4.3125

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 = -4.3125 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.3125 + 6.25

Combine like terms: -4.3125 + 6.25 = 1.9375
6.25 + -5x + x2 = 1.9375

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.9375

Calculate the square root of the right side: 1.391941091

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.391941091 and -1.391941091.

Subproblem 1

x + -2.5 = 1.391941091 Simplifying x + -2.5 = 1.391941091 Reorder the terms: -2.5 + x = 1.391941091 Solving -2.5 + x = 1.391941091 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 = 1.391941091 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.391941091 + 2.5 x = 1.391941091 + 2.5 Combine like terms: 1.391941091 + 2.5 = 3.891941091 x = 3.891941091 Simplifying x = 3.891941091

Subproblem 2

x + -2.5 = -1.391941091 Simplifying x + -2.5 = -1.391941091 Reorder the terms: -2.5 + x = -1.391941091 Solving -2.5 + x = -1.391941091 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 = -1.391941091 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.391941091 + 2.5 x = -1.391941091 + 2.5 Combine like terms: -1.391941091 + 2.5 = 1.108058909 x = 1.108058909 Simplifying x = 1.108058909

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.891941091, 1.108058909}

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