6X^2-30X+18=

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Solution for 6X^2-30X+18= equation:


Simplifying
6X2 + -30X + 18 = 0

Reorder the terms:
18 + -30X + 6X2 = 0

Solving
18 + -30X + 6X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3 + -5X + X2) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(3 + -5X + X2)' equal to zero and attempt to solve: Simplifying 3 + -5X + X2 = 0 Solving 3 + -5X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5X + -3 + X2 = 0 + -3 Reorder the terms: 3 + -3 + -5X + X2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5X + X2 = 0 + -3 -5X + X2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5X + X2 = -3 The X term is -5X. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5X + 6.25 + X2 = -3 + 6.25 Reorder the terms: 6.25 + -5X + X2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5X + X2 = 3.25 Factor a perfect square on the left side: (X + -2.5)(X + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (X + -2.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

X + -2.5 = 1.802775638 Simplifying X + -2.5 = 1.802775638 Reorder the terms: -2.5 + X = 1.802775638 Solving -2.5 + X = 1.802775638 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = 1.802775638 + 2.5 X = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 X = 4.302775638 Simplifying X = 4.302775638

Subproblem 2

X + -2.5 = -1.802775638 Simplifying X + -2.5 = -1.802775638 Reorder the terms: -2.5 + X = -1.802775638 Solving -2.5 + X = -1.802775638 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + X = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + X = -1.802775638 + 2.5 X = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 X = 0.697224362 Simplifying X = 0.697224362

Solution

The solution to the problem is based on the solutions from the subproblems. X = {4.302775638, 0.697224362}

Solution

X = {4.302775638, 0.697224362}

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