0=-16x^2+18x+5

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Solution for 0=-16x^2+18x+5 equation:


Simplifying
0 = -16x2 + 18x + 5

Reorder the terms:
0 = 5 + 18x + -16x2

Solving
0 = 5 + 18x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -18x + 16x2 = 5 + 18x + -16x2 + -5 + -18x + 16x2

Reorder the terms:
-5 + -18x + 16x2 = 5 + -5 + 18x + -18x + -16x2 + 16x2

Combine like terms: 5 + -5 = 0
-5 + -18x + 16x2 = 0 + 18x + -18x + -16x2 + 16x2
-5 + -18x + 16x2 = 18x + -18x + -16x2 + 16x2

Combine like terms: 18x + -18x = 0
-5 + -18x + 16x2 = 0 + -16x2 + 16x2
-5 + -18x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-5 + -18x + 16x2 = 0

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

Divide each side by '16'.
-0.3125 + -1.125x + x2 = 0

Move the constant term to the right:

Add '0.3125' to each side of the equation.
-0.3125 + -1.125x + 0.3125 + x2 = 0 + 0.3125

Reorder the terms:
-0.3125 + 0.3125 + -1.125x + x2 = 0 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + -1.125x + x2 = 0 + 0.3125
-1.125x + x2 = 0 + 0.3125

Combine like terms: 0 + 0.3125 = 0.3125
-1.125x + x2 = 0.3125

The x term is -1.125x.  Take half its coefficient (-0.5625).
Square it (0.31640625) and add it to both sides.

Add '0.31640625' to each side of the equation.
-1.125x + 0.31640625 + x2 = 0.3125 + 0.31640625

Reorder the terms:
0.31640625 + -1.125x + x2 = 0.3125 + 0.31640625

Combine like terms: 0.3125 + 0.31640625 = 0.62890625
0.31640625 + -1.125x + x2 = 0.62890625

Factor a perfect square on the left side:
(x + -0.5625)(x + -0.5625) = 0.62890625

Calculate the square root of the right side: 0.793036096

Break this problem into two subproblems by setting 
(x + -0.5625) equal to 0.793036096 and -0.793036096.

Subproblem 1

x + -0.5625 = 0.793036096 Simplifying x + -0.5625 = 0.793036096 Reorder the terms: -0.5625 + x = 0.793036096 Solving -0.5625 + x = 0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = 0.793036096 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = 0.793036096 + 0.5625 x = 0.793036096 + 0.5625 Combine like terms: 0.793036096 + 0.5625 = 1.355536096 x = 1.355536096 Simplifying x = 1.355536096

Subproblem 2

x + -0.5625 = -0.793036096 Simplifying x + -0.5625 = -0.793036096 Reorder the terms: -0.5625 + x = -0.793036096 Solving -0.5625 + x = -0.793036096 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + x = -0.793036096 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + x = -0.793036096 + 0.5625 x = -0.793036096 + 0.5625 Combine like terms: -0.793036096 + 0.5625 = -0.230536096 x = -0.230536096 Simplifying x = -0.230536096

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.355536096, -0.230536096}

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