Question

Quadratic formula. pls help

Answer 1

`x=-1,(5)/(7)`

Explanation:

1) Split the second term in
`7{x}^(2)+2x-5` into two terms.

1 - Multiply the coefficient of the first term by the constant term.

`7* -5=-35`

2 - Ask: Which two numbers add up to 2 and multiply to -35?

7 and -5.

3 - Split 2x as the sum of 7x and -5x.

`7x^2+7x-5x-5`

2) Factor out common terms in the first two terms, then in the last two terms.

`7x(x+1)-5(x+1)=0`

3) Factor out the common term x+1.

`(x+1)(7x-5)=0`

4) Solve for x.

1 - Ask: When will (x+1)(7x-5) equal zero?

When x + 1 0 or 7x-5=0

2 - Solve each of the 2 equations above.

`x=-1,(5)/(7)`

Answer 2

`\huge\text{Hey there!}`

`\huge\textbf{What are the quadratic formulas?}`

`\bullet\rm{\ (-b \pm √(b^2 - 4ac))/(2a)}`

`\bullet\rm{\ ax^2 + bx + c = 0}`

`\huge\textbf{What are we solving for?}`

`\rm{7x^2 + 2x - 5 = 0}`

`\huge\textbf{What do we have to do?}`

`\rm{7x^2 + 2x - 5 = 0}`

`\huge\textbf{Factor the LEFT side of the given}\\\\\huge\textbf{equation:}`

`\rm{(7x - 5)(x + 1) = 0}`

`\rm{(7x - 5) * (x + 1) = 0}`

`\huge\textbf{Set 0 to the factors:}`

`\rm{7x - 5 = 0\ or\ x + 1 = 0}`

`\huge\textbf{Simplify it:}`

`\rm{x = (5)/(7)\ or\ x = -1}`

`\huge\textbf{Therefore, your answer should be:}`

`\huge\boxed{\frak{\mathsf x = (5)/(7)\ or\ \mathsf{x} = -1}}\huge\checkmark`

~
`\frak{Amphitrite1040:)}`