3x^2-45x=-10

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Solution for 3x^2-45x=-10 equation:


Simplifying
3x2 + -45x = -10

Reorder the terms:
-45x + 3x2 = -10

Solving
-45x + 3x2 = -10

Solving for variable 'x'.

Reorder the terms:
10 + -45x + 3x2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + -45x + 3x2 = 0

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

Divide each side by '3'.
3.333333333 + -15x + x2 = 0

Move the constant term to the right:

Add '-3.333333333' to each side of the equation.
3.333333333 + -15x + -3.333333333 + x2 = 0 + -3.333333333

Reorder the terms:
3.333333333 + -3.333333333 + -15x + x2 = 0 + -3.333333333

Combine like terms: 3.333333333 + -3.333333333 = 0.000000000
0.000000000 + -15x + x2 = 0 + -3.333333333
-15x + x2 = 0 + -3.333333333

Combine like terms: 0 + -3.333333333 = -3.333333333
-15x + x2 = -3.333333333

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = -3.333333333 + 56.25

Reorder the terms:
56.25 + -15x + x2 = -3.333333333 + 56.25

Combine like terms: -3.333333333 + 56.25 = 52.916666667
56.25 + -15x + x2 = 52.916666667

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 52.916666667

Calculate the square root of the right side: 7.274384281

Break this problem into two subproblems by setting 
(x + -7.5) equal to 7.274384281 and -7.274384281.

Subproblem 1

x + -7.5 = 7.274384281 Simplifying x + -7.5 = 7.274384281 Reorder the terms: -7.5 + x = 7.274384281 Solving -7.5 + x = 7.274384281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 7.274384281 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 7.274384281 + 7.5 x = 7.274384281 + 7.5 Combine like terms: 7.274384281 + 7.5 = 14.774384281 x = 14.774384281 Simplifying x = 14.774384281

Subproblem 2

x + -7.5 = -7.274384281 Simplifying x + -7.5 = -7.274384281 Reorder the terms: -7.5 + x = -7.274384281 Solving -7.5 + x = -7.274384281 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -7.274384281 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -7.274384281 + 7.5 x = -7.274384281 + 7.5 Combine like terms: -7.274384281 + 7.5 = 0.225615719 x = 0.225615719 Simplifying x = 0.225615719

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.774384281, 0.225615719}

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