3x^2-6x-21=0

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Solution for 3x^2-6x-21=0 equation:


Simplifying
3x2 + -6x + -21 = 0

Reorder the terms:
-21 + -6x + 3x2 = 0

Solving
-21 + -6x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-7 + -2x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-7 + -2x + x2)' equal to zero and attempt to solve: Simplifying -7 + -2x + x2 = 0 Solving -7 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -2x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -2x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -2x + x2 = 0 + 7 -2x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -2x + x2 = 7 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 = 7 + 1 Reorder the terms: 1 + -2x + x2 = 7 + 1 Combine like terms: 7 + 1 = 8 1 + -2x + x2 = 8 Factor a perfect square on the left side: (x + -1)(x + -1) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + -1 = 2.828427125 Simplifying x + -1 = 2.828427125 Reorder the terms: -1 + x = 2.828427125 Solving -1 + x = 2.828427125 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 = 2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.828427125 + 1 x = 2.828427125 + 1 Combine like terms: 2.828427125 + 1 = 3.828427125 x = 3.828427125 Simplifying x = 3.828427125

Subproblem 2

x + -1 = -2.828427125 Simplifying x + -1 = -2.828427125 Reorder the terms: -1 + x = -2.828427125 Solving -1 + x = -2.828427125 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 = -2.828427125 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.828427125 + 1 x = -2.828427125 + 1 Combine like terms: -2.828427125 + 1 = -1.828427125 x = -1.828427125 Simplifying x = -1.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.828427125, -1.828427125}

Solution

x = {3.828427125, -1.828427125}

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