ASAP please help algebra 1

Question

Part A: Solve the equation to determine the solutions. Is it Ms. Jackson's document? If not, what are the correct solutions to the problem on this document? *

you come across another document with the following function, 16x^2 +10x - 27 = -6x+5 and wonder if it might have belonged to mary jackson basd on a previous interview ms jackson recalled that she was missing a document with an equation that had 3 as one of its solutions could this document be ms jacksons missing document? explain your answer. solve by factoring

Answer 1

Solved using Factoring

16x² + 10x - 27 = -6x + 5 (Set your quadratic equation equal to zero in order to factor)

16x² + 10x - 32 = -6x (subtract 5 on both sides)

16x² + 16x - 32 = 0 (add 6x to both sides)

16x² + 16x - 32 = 0

16 (x² + 1x - 2) = 0 (Remove a GCF of 16)

Find 2 integers that multiply to c (which is -2) and add to b (which is 1).

2 * -1 = -2 and 2 + -1 = 1

So,

16 (x + 2)(x - 1) = 0 (Factored form)

Apply the zero product property,

x + 2 = 0 and x - 1 = 0

Therefore,

x = -2 and x = 1

Solution: It is not one of Ms. Jackson's solutions because neither solution is equal to 3. The correct solutions are -2 and 1.

Answer 2

16x² + 10x - 27 = -6x + 5

16x² + 10x -27 + 6x - 5

16x² +16x - 32 = 0

Quadratic formula: x_{1, 2} = (-b ± √b² - 4ac) / 2a

x_{1, 2} = (-16 ± √16² - 4*16*(-32)) / 2*16

x_{1, 2} = (-16 ± 48) / 32

x₁ = (-16 + 48) / 32

x₁ = 1

x₂ = (-16 - 48) / 32

x₂ = -2

This document could NOT be Ms Jackson's missing document, because the solutions of this document are 1 and -2. And, Ms Jackson's document has an equation with 3 as one of its solutions.