# Use factoring and the zero product property to solve the following problem. x^2 - x - 10 = 2

Asked on by loishy

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to move the term 2 to the left side, such that:

`x^2 - x - 10 - 2 = 0`

`x^2 - x - 12 = 0 => x^2 - x - 9 - 3 = 0`

You need to group the terms such that:

`(x^2 - 9) - (x + 3) = 0`

You need to convert the difference of squares `x^2 - 9` , into a product, such that:

`x^2 - 9 = (x - 3)(x + 3)`

`(x - 3)(x + 3) - (x + 3) = 0 => (x + 3)(x - 3 - 1) = 0`

`(x + 3)(x - 4) = 0 => {(x + 3 = 0),(x - 4 = 0):}`

`{(x = -3),(x = 4):}`

Hence, evaluating the solution to quadratic equation, using factorization, yields `x = -3, x = 4.`

pramodpandey | College Teacher | (Level 3) Valedictorian

Posted on

`x^2-x-10=2`

`x^2-x-10-2=0`

`x^2-x-12=0`

Factor 12 into two parts ,whose difference is 1

`12=4xx3`

`4-3=1`

`x^2-(4-1)x-12=0`

`x^2-4x+3x-12=0`

`` Factor out x from first two terms and 3 from last two terms

`x(x-4)+3(x-4)=0`

`(x-4)(x+3)=0`

`x=4` ,-3

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