3x^2-6x=30

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Solution for 3x^2-6x=30 equation:


Simplifying
3x2 + -6x = 30

Reorder the terms:
-6x + 3x2 = 30

Solving
-6x + 3x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + -6x + 3x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -2x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-10 + -2x + x2)' equal to zero and attempt to solve: Simplifying -10 + -2x + x2 = 0 Solving -10 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -2x + x2 = 0 + 10 -2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -2x + x2 = 10 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + -2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + -2x + x2 = 11 Factor a perfect square on the left side: (x + -1)(x + -1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1

x + -1 = 3.31662479 Simplifying x + -1 = 3.31662479 Reorder the terms: -1 + x = 3.31662479 Solving -1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.31662479 + 1 x = 3.31662479 + 1 Combine like terms: 3.31662479 + 1 = 4.31662479 x = 4.31662479 Simplifying x = 4.31662479

Subproblem 2

x + -1 = -3.31662479 Simplifying x + -1 = -3.31662479 Reorder the terms: -1 + x = -3.31662479 Solving -1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.31662479 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.31662479 + 1 x = -3.31662479 + 1 Combine like terms: -3.31662479 + 1 = -2.31662479 x = -2.31662479 Simplifying x = -2.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.31662479, -2.31662479}

Solution

x = {4.31662479, -2.31662479}

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