Question

6 X square 2 +60x+150=0​

Answer 1

Answer:

Simplifying

6x2 + -60x + 150 = 0

Reorder the terms:

150 + -60x + 6x2 = 0

Solving

150 + -60x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.

6(25 + -10x + x2) = 0

Factor a trinomial.

6((5 + -1x)(5 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying

5 + -1x = 0

Solving

5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.

5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0

0 + -1x = 0 + -5

-1x = 0 + -5

Combine like terms: 0 + -5 = -5

-1x = -5

Divide each side by '-1'.

x = 5

Simplifying

x = 5

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying

5 + -1x = 0

Solving

5 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.

5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0

0 + -1x = 0 + -5

-1x = 0 + -5

Combine like terms: 0 + -5 = -5

-1x = -5

Divide each side by '-1'.

x = 5

Simplifying

x = 5

Solution

x = {5, 5}

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Answer 2

Answer:

$6x {}^{2} + 60x + 150 = 0 \\ 6(x {}^{2} + 10x + 25) = 0 \\ x {}^{2} + 10x + 25 = 0 \\ x {}^{2} + 5x + 5x + 25 = 0 \\x(x + 5) + 5(x + 5) = 0 \\( x + 5)(x + 5) = 0 \\ x + 5 = 0 \\ x = - 5$

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