Question

Quadratic formula. pls help

Answer 1

Answer:

$x=-1,\frac{5}{7}$

Step-by-step 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.

$7\times -5=-35$

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.

$x=-1,\frac{5}{7}$

Answer 2

$\huge\text{Hey there!}$

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

$\bullet\rm{\ \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}}$

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

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

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

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

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

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

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

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

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

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

$\huge\textbf{Simplify it:}$

$\rm{x = \dfrac{5}{7}\ or\ x = -1}$

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

$\huge\boxed{\frak{\mathsf x = \dfrac{5}{7}\ or\ \mathsf{x} = -1}}\huge\checkmark$

$\huge\text{Good luck on your assignment \& enjoy your day!}$

~$\frak{Amphitrite1040:)}$