2(x-6)(x-2)=4

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Solution for 2(x-6)(x-2)=4 equation:


Simplifying
2(x + -6)(x + -2) = 4

Reorder the terms:
2(-6 + x)(x + -2) = 4

Reorder the terms:
2(-6 + x)(-2 + x) = 4

Multiply (-6 + x) * (-2 + x)
2(-6(-2 + x) + x(-2 + x)) = 4
2((-2 * -6 + x * -6) + x(-2 + x)) = 4
2((12 + -6x) + x(-2 + x)) = 4
2(12 + -6x + (-2 * x + x * x)) = 4
2(12 + -6x + (-2x + x2)) = 4

Combine like terms: -6x + -2x = -8x
2(12 + -8x + x2) = 4
(12 * 2 + -8x * 2 + x2 * 2) = 4
(24 + -16x + 2x2) = 4

Solving
24 + -16x + 2x2 = 4

Solving for variable 'x'.

Reorder the terms:
24 + -4 + -16x + 2x2 = 4 + -4

Combine like terms: 24 + -4 = 20
20 + -16x + 2x2 = 4 + -4

Combine like terms: 4 + -4 = 0
20 + -16x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -8x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(10 + -8x + x2)' equal to zero and attempt to solve: Simplifying 10 + -8x + x2 = 0 Solving 10 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + -8x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -8x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -8x + x2 = 0 + -10 -8x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -8x + x2 = -10 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -10 + 16 Reorder the terms: 16 + -8x + x2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + -8x + x2 = 6 Factor a perfect square on the left side: (x + -4)(x + -4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -4) equal to 2.449489743 and -2.449489743.

Subproblem 1

x + -4 = 2.449489743 Simplifying x + -4 = 2.449489743 Reorder the terms: -4 + x = 2.449489743 Solving -4 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = 2.449489743 + 4 x = 2.449489743 + 4 Combine like terms: 2.449489743 + 4 = 6.449489743 x = 6.449489743 Simplifying x = 6.449489743

Subproblem 2

x + -4 = -2.449489743 Simplifying x + -4 = -2.449489743 Reorder the terms: -4 + x = -2.449489743 Solving -4 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -2.449489743 + 4 Combine like terms: -4 + 4 = 0 0 + x = -2.449489743 + 4 x = -2.449489743 + 4 Combine like terms: -2.449489743 + 4 = 1.550510257 x = 1.550510257 Simplifying x = 1.550510257

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.449489743, 1.550510257}

Solution

x = {6.449489743, 1.550510257}

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