3(x*x+2*x*2+2*2)-21=0

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Solution for 3(x*x+2*x*2+2*2)-21=0 equation:


Simplifying
3(x * x + 2x * 2 + 2 * 2) + -21 = 0

Multiply x * x
3(x2 + 2x * 2 + 2 * 2) + -21 = 0

Reorder the terms for easier multiplication:
3(x2 + 2 * 2x + 2 * 2) + -21 = 0

Multiply 2 * 2
3(x2 + 4x + 2 * 2) + -21 = 0

Multiply 2 * 2
3(x2 + 4x + 4) + -21 = 0

Reorder the terms:
3(4 + 4x + x2) + -21 = 0
(4 * 3 + 4x * 3 + x2 * 3) + -21 = 0
(12 + 12x + 3x2) + -21 = 0

Reorder the terms:
12 + -21 + 12x + 3x2 = 0

Combine like terms: 12 + -21 = -9
-9 + 12x + 3x2 = 0

Solving
-9 + 12x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-3 + 4x + x2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + 4x + x2)' equal to zero and attempt to solve: Simplifying -3 + 4x + x2 = 0 Solving -3 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 4x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 4x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4x + x2 = 0 + 3 4x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 4x + x2 = 3 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 3 + 4 Reorder the terms: 4 + 4x + x2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4x + x2 = 7 Factor a perfect square on the left side: (x + 2)(x + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + 2) equal to 2.645751311 and -2.645751311.

Subproblem 1

x + 2 = 2.645751311 Simplifying x + 2 = 2.645751311 Reorder the terms: 2 + x = 2.645751311 Solving 2 + x = 2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.645751311 + -2 x = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 x = 0.645751311 Simplifying x = 0.645751311

Subproblem 2

x + 2 = -2.645751311 Simplifying x + 2 = -2.645751311 Reorder the terms: 2 + x = -2.645751311 Solving 2 + x = -2.645751311 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.645751311 + -2 x = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 x = -4.645751311 Simplifying x = -4.645751311

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.645751311, -4.645751311}

Solution

x = {0.645751311, -4.645751311}

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