Question

4x^2-14x=-2-5x solve by factoring

Answer 1

`x\text{ = 2 or x = }(1)/(4)\text{ and the factors of the function are; \lparen x - 2\rparen \lparen4x - 1\rparen}`

Step-by-step explanation

Given equation

`4x^2\text{ - 14x = -2 - 5x}`

To factorize the given equation, follow the steps below

Step 1: Re-arrange the equation

`\begin{gathered} 4x^2\text{ - 14x = -2 - 5x} \\ 4x^2\text{ - 14x + 2 + 5x = 0} \\ 4x^2\text{ - 14x + 5x + 2 =0} \\ 4x^2\text{ - 9x + 2 = 0} \end{gathered}`

Step 2: Relate the equation to the general form of a quadratic function

`\begin{gathered} \text{ The general quadratic function is given as} \\ \text{ ax}^2+bx\text{ + c = 0} \\ \text{ 4x}^2\text{ - 9x + 2 = 0} \\ \text{ Relating the two functions together, we will have the following data} \\ a\text{ = 4} \\ b\text{ = -9} \\ c\text{ = 2} \end{gathered}`

Step 3: Find ac

`\begin{gathered} ac\text{ = 4 }*\text{ 2} \\ \text{ ac = 8} \end{gathered}`

Step 4: Find the factors of 8 that will give -9 when added and +8 when multiplied.

The factors are -1 and - 8

Step 5: Factorize the above-given function

`\begin{gathered} \text{ 4x}^2\text{ - x - 8x + 2 = 0} \\ x(4x\text{ - 1\rparen-2\lparen4x - 1\rparen = 0} \\ (x\text{ - 2\rparen \lparen4x - 1\rparen = 0} \\ (x\text{ - 2\rparen = 0 or \lparen4x - 1\rparen = 0} \\ x\text{ = 2 or x = }(1)/(4) \end{gathered}`