5x^2-3=6x

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Solution for 5x^2-3=6x equation:


Simplifying
5x2 + -3 = 6x

Reorder the terms:
-3 + 5x2 = 6x

Solving
-3 + 5x2 = 6x

Solving for variable 'x'.

Reorder the terms:
-3 + -6x + 5x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-3 + -6x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -1.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -1.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -1.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -1.2x + x2 = 0 + 0.6
-1.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-1.2x + x2 = 0.6

The x term is -1.2x.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2x + 0.36 + x2 = 0.6 + 0.36

Reorder the terms:
0.36 + -1.2x + x2 = 0.6 + 0.36

Combine like terms: 0.6 + 0.36 = 0.96
0.36 + -1.2x + x2 = 0.96

Factor a perfect square on the left side:
(x + -0.6)(x + -0.6) = 0.96

Calculate the square root of the right side: 0.979795897

Break this problem into two subproblems by setting 
(x + -0.6) equal to 0.979795897 and -0.979795897.

Subproblem 1

x + -0.6 = 0.979795897 Simplifying x + -0.6 = 0.979795897 Reorder the terms: -0.6 + x = 0.979795897 Solving -0.6 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.979795897 + 0.6 x = 0.979795897 + 0.6 Combine like terms: 0.979795897 + 0.6 = 1.579795897 x = 1.579795897 Simplifying x = 1.579795897

Subproblem 2

x + -0.6 = -0.979795897 Simplifying x + -0.6 = -0.979795897 Reorder the terms: -0.6 + x = -0.979795897 Solving -0.6 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.979795897 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.979795897 + 0.6 x = -0.979795897 + 0.6 Combine like terms: -0.979795897 + 0.6 = -0.379795897 x = -0.379795897 Simplifying x = -0.379795897

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.579795897, -0.379795897}

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