-16x^2+64x+23=0

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Solution for -16x^2+64x+23=0 equation:


Simplifying
-16x2 + 64x + 23 = 0

Reorder the terms:
23 + 64x + -16x2 = 0

Solving
23 + 64x + -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'.
-1.4375 + -4x + x2 = 0

Move the constant term to the right:

Add '1.4375' to each side of the equation.
-1.4375 + -4x + 1.4375 + x2 = 0 + 1.4375

Reorder the terms:
-1.4375 + 1.4375 + -4x + x2 = 0 + 1.4375

Combine like terms: -1.4375 + 1.4375 = 0.0000
0.0000 + -4x + x2 = 0 + 1.4375
-4x + x2 = 0 + 1.4375

Combine like terms: 0 + 1.4375 = 1.4375
-4x + x2 = 1.4375

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 1.4375 + 4

Reorder the terms:
4 + -4x + x2 = 1.4375 + 4

Combine like terms: 1.4375 + 4 = 5.4375
4 + -4x + x2 = 5.4375

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5.4375

Calculate the square root of the right side: 2.331844763

Break this problem into two subproblems by setting 
(x + -2) equal to 2.331844763 and -2.331844763.

Subproblem 1

x + -2 = 2.331844763 Simplifying x + -2 = 2.331844763 Reorder the terms: -2 + x = 2.331844763 Solving -2 + x = 2.331844763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 2.331844763 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.331844763 + 2 x = 2.331844763 + 2 Combine like terms: 2.331844763 + 2 = 4.331844763 x = 4.331844763 Simplifying x = 4.331844763

Subproblem 2

x + -2 = -2.331844763 Simplifying x + -2 = -2.331844763 Reorder the terms: -2 + x = -2.331844763 Solving -2 + x = -2.331844763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -2.331844763 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.331844763 + 2 x = -2.331844763 + 2 Combine like terms: -2.331844763 + 2 = -0.331844763 x = -0.331844763 Simplifying x = -0.331844763

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.331844763, -0.331844763}

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