(3X-9)(3X-9)=12

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Solution for (3X-9)(3X-9)=12 equation:


Simplifying
(3X + -9)(3X + -9) = 12

Reorder the terms:
(-9 + 3X)(3X + -9) = 12

Reorder the terms:
(-9 + 3X)(-9 + 3X) = 12

Multiply (-9 + 3X) * (-9 + 3X)
(-9(-9 + 3X) + 3X * (-9 + 3X)) = 12
((-9 * -9 + 3X * -9) + 3X * (-9 + 3X)) = 12
((81 + -27X) + 3X * (-9 + 3X)) = 12
(81 + -27X + (-9 * 3X + 3X * 3X)) = 12
(81 + -27X + (-27X + 9X2)) = 12

Combine like terms: -27X + -27X = -54X
(81 + -54X + 9X2) = 12

Solving
81 + -54X + 9X2 = 12

Solving for variable 'X'.

Reorder the terms:
81 + -12 + -54X + 9X2 = 12 + -12

Combine like terms: 81 + -12 = 69
69 + -54X + 9X2 = 12 + -12

Combine like terms: 12 + -12 = 0
69 + -54X + 9X2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(23 + -18X + 3X2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(23 + -18X + 3X2)' equal to zero and attempt to solve: Simplifying 23 + -18X + 3X2 = 0 Solving 23 + -18X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 7.666666667 + -6X + X2 = 0 Move the constant term to the right: Add '-7.666666667' to each side of the equation. 7.666666667 + -6X + -7.666666667 + X2 = 0 + -7.666666667 Reorder the terms: 7.666666667 + -7.666666667 + -6X + X2 = 0 + -7.666666667 Combine like terms: 7.666666667 + -7.666666667 = 0.000000000 0.000000000 + -6X + X2 = 0 + -7.666666667 -6X + X2 = 0 + -7.666666667 Combine like terms: 0 + -7.666666667 = -7.666666667 -6X + X2 = -7.666666667 The X term is -6X. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6X + 9 + X2 = -7.666666667 + 9 Reorder the terms: 9 + -6X + X2 = -7.666666667 + 9 Combine like terms: -7.666666667 + 9 = 1.333333333 9 + -6X + X2 = 1.333333333 Factor a perfect square on the left side: (X + -3)(X + -3) = 1.333333333 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (X + -3) equal to 1.154700538 and -1.154700538.

Subproblem 1

X + -3 = 1.154700538 Simplifying X + -3 = 1.154700538 Reorder the terms: -3 + X = 1.154700538 Solving -3 + X = 1.154700538 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = 1.154700538 + 3 Combine like terms: -3 + 3 = 0 0 + X = 1.154700538 + 3 X = 1.154700538 + 3 Combine like terms: 1.154700538 + 3 = 4.154700538 X = 4.154700538 Simplifying X = 4.154700538

Subproblem 2

X + -3 = -1.154700538 Simplifying X + -3 = -1.154700538 Reorder the terms: -3 + X = -1.154700538 Solving -3 + X = -1.154700538 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + X = -1.154700538 + 3 Combine like terms: -3 + 3 = 0 0 + X = -1.154700538 + 3 X = -1.154700538 + 3 Combine like terms: -1.154700538 + 3 = 1.845299462 X = 1.845299462 Simplifying X = 1.845299462

Solution

The solution to the problem is based on the solutions from the subproblems. X = {4.154700538, 1.845299462}

Solution

X = {4.154700538, 1.845299462}

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