3.15x-3=0.3x^2

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Solution for 3.15x-3=0.3x^2 equation:


Simplifying
3.15x + -3 = 0.3x2

Reorder the terms:
-3 + 3.15x = 0.3x2

Solving
-3 + 3.15x = 0.3x2

Solving for variable 'x'.

Combine like terms: 0.3x2 + -0.3x2 = 0.0
-3 + 3.15x + -0.3x2 = 0.0

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
10 + -10.5x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -10.5x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -10.5x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -10.5x + x2 = 0 + -10
-10.5x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-10.5x + x2 = -10

The x term is -10.5x.  Take half its coefficient (-5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
-10.5x + 27.5625 + x2 = -10 + 27.5625

Reorder the terms:
27.5625 + -10.5x + x2 = -10 + 27.5625

Combine like terms: -10 + 27.5625 = 17.5625
27.5625 + -10.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -5.25)(x + -5.25) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -5.25) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + -5.25 = 4.190763654 Simplifying x + -5.25 = 4.190763654 Reorder the terms: -5.25 + x = 4.190763654 Solving -5.25 + x = 4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 4.190763654 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 4.190763654 + 5.25 x = 4.190763654 + 5.25 Combine like terms: 4.190763654 + 5.25 = 9.440763654 x = 9.440763654 Simplifying x = 9.440763654

Subproblem 2

x + -5.25 = -4.190763654 Simplifying x + -5.25 = -4.190763654 Reorder the terms: -5.25 + x = -4.190763654 Solving -5.25 + x = -4.190763654 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -4.190763654 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -4.190763654 + 5.25 x = -4.190763654 + 5.25 Combine like terms: -4.190763654 + 5.25 = 1.059236346 x = 1.059236346 Simplifying x = 1.059236346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.440763654, 1.059236346}

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