What is the greatest solution of x in the equation x2 + 8x - 30 = 18? Enter your answer in the box.

9514 1404 393

  x = 4

Step-by-step explanation:

Subtracting 18,  we have the equation ...

  x^2 +8x -48 = 0

  (x +12)(x -4) = 0 . . . . . factored form

The values of x that make these factors zero are the solutions:

  x = -12, x = 4

The greatest solution is x=4.

Greatest solution of x = 4

Step-by-step explanation:

x² + 8x - 30 = 18

subtract 18 from both sides

x² + 8 x - 30 - 18 = 18 - 18

x ² + 8 x - 48 = 0

split 8x in middle form

x² + ( 12 x - 4 x ) - 48 = 0

factor out x from the first pair

x ( x + 12 ) - ( 4 x- 48 ) = 0

factor out 4 from the second pair

x ( x + 12) - 4 ( x + 12 ) = 0

x + 12 is common factor

x ( x + 12) - 4 ( x + 12 ) = 0

Group common factor

(x - 4) ( x + 12 ) = 0

When the product of factors equal 0, at least one factor is 0.

x - 4 = 0

x = 4

similarly,

x + 12 = 0

x = - 12

Greatest solution of x = 4

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