# TSI Math: Solving a Quadratic Equation through Grouping

Which of the following values is a root of the equation 10x² = 37x – 7?

Intermediate Algebra and Functions | Quadratic and Other Polynomial Expressions, Equations, and Functions |

Mathematics and Statistics Assessment | Quadratic and Other Polynomial Expressions, and Functions |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Intermediate Algebra and Functions |

TSI Mathematics | Intermediate Algebra and Functions |

Test Prep | TSI |

### Transcript

Ten x squared plus thirty seven x minus seven is

zero See we've zero fight it then we could use

the quadratic formula here but well we'll solve this equation

by grouping instead It's probably easier when the coefficient of

x squared isn't one like here It's ten or negative

ten Actually the first step is to multiply the coefficient

of x squared by the constant term Well here we

get negative ten times Negative seven which makes positive seventy

Now we need to think of two factors of this

result here for seventy which add up to thirty seven

So what could it be Yeah two times thirty five

is seventy and two plus thirty five is thirty seven

So pretty easy so we can rewrite This is thirty

seven x thing here is to Acts plus 35 acts

that'll help on the fact arising thing here So we're

then gonna factor to acts from the group to simplify

things a tad and we get well to x out

here that multiplies through the negative five x plus one

and then we've got the multiplying by negative seven times

the quantity negative five expose one equal zero we've got

negative five x plus one inside each parentheses here is

very clever very hard to dio Very hard to recognize

but hopefully you got it Okay so yes are factoring

was successful and now we're going to factor out the

negative five x plus one So we get that over

here on the left and then we're going to multiply

it by two x minus seven to get zero Well

the roots can be found by setting each of the

expressions in parentheses equals zero and just solving for x

Right So that gets us negative Five Acts plus 1

equals 0 and while we can subtract one from both

sides there we get negative five x equals negative one

Divide both sides by negative five and we get x

equals a fifth So whoa hold up That happens to

be be so we've technically found our answer However never

let it be said we don't finish what we start

to find the other route I'll do the same with

two x minus seven thereby adding seven on both sides

we get to act Sequel seven in the nexus seven

abs This is a positive value not the negative values

seen in negative seven halves there So give it up

either So the answer is b it's one fifth and 00:02:32.903 --> [endTime] that is in fact a route of that equation