5x^2-16x=9

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Solution for 5x^2-16x=9 equation:


Simplifying
5x2 + -16x = 9

Reorder the terms:
-16x + 5x2 = 9

Solving
-16x + 5x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + -16x + 5x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -16x + 5x2 = 0

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

Divide each side by '5'.
-1.8 + -3.2x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -3.2x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -3.2x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -3.2x + x2 = 0 + 1.8
-3.2x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-3.2x + x2 = 1.8

The x term is -3.2x.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2x + 2.56 + x2 = 1.8 + 2.56

Reorder the terms:
2.56 + -3.2x + x2 = 1.8 + 2.56

Combine like terms: 1.8 + 2.56 = 4.36
2.56 + -3.2x + x2 = 4.36

Factor a perfect square on the left side:
(x + -1.6)(x + -1.6) = 4.36

Calculate the square root of the right side: 2.088061302

Break this problem into two subproblems by setting 
(x + -1.6) equal to 2.088061302 and -2.088061302.

Subproblem 1

x + -1.6 = 2.088061302 Simplifying x + -1.6 = 2.088061302 Reorder the terms: -1.6 + x = 2.088061302 Solving -1.6 + x = 2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.088061302 + 1.6 x = 2.088061302 + 1.6 Combine like terms: 2.088061302 + 1.6 = 3.688061302 x = 3.688061302 Simplifying x = 3.688061302

Subproblem 2

x + -1.6 = -2.088061302 Simplifying x + -1.6 = -2.088061302 Reorder the terms: -1.6 + x = -2.088061302 Solving -1.6 + x = -2.088061302 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.088061302 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.088061302 + 1.6 x = -2.088061302 + 1.6 Combine like terms: -2.088061302 + 1.6 = -0.488061302 x = -0.488061302 Simplifying x = -0.488061302

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.688061302, -0.488061302}

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