Chapter 9.1, Problem 7PSA

a

To determine

To calculate: The Value of xin the given expression i.e. $x^2-5x-6=0$

Answer to Problem 7PSA

Values of x are $-1$ and $6$ .

Explanation of Solution

Given information:$x^2-5x-6=0$

Calculation: $x^2-5x-6=0$

  $\begin{array}{l}\Rightarrow x^2-6x+x-6=0\\ \Rightarrow x(x-6)+1(x-6)=0\end{array}$

  $\Rightarrow x+1=0$ and $x-6=0$

  $\Rightarrow x=-1$ and $x=6$

b

To determine

To calculate: The Value of xin the given expression i.e. $x^2+4x-12=0$

Answer to Problem 7PSA

Values of x are $2$ and $-6$ .

Explanation of Solution

Given information:$x^2+4x-12=0$

Calculation: $x^2+4x-12=0$

  $\begin{array}{l}\Rightarrow x^2+6x-2x-12=0\\ \Rightarrow x(x+6)-2(x+6)=0\end{array}$

  $\Rightarrow x-2=0$ and $x+6=0$

  $\Rightarrow x=2$ and $x=-6$

c

To determine

To calculate: The Value of xin the given expression i.e. $x^2-8x+15=0$

Answer to Problem 7PSA

Values of x are $5$ and $3$ .

Explanation of Solution

Given information:$x^2-8x+15=0$

Calculation: $x^2-8x+15=0$

  $\begin{array}{l}\Rightarrow x^2-3x-5x+15=0\\ \Rightarrow x(x-3)-5(x-3)=0\end{array}$

  $\Rightarrow x-5=0$ and $x-3=0$

  $\Rightarrow x=5$ and $x=3$

d

To determine

To calculate: The Value of xin the given expression i.e. $x^2-18-3x=0$

Answer to Problem 7PSA

Values of x are $-3$ and $6$ .

Explanation of Solution

Given information:$x^2-18-3x=0$

Calculation: $x^2-18-3x=0$

  $\begin{array}{l}\Rightarrow x^2-3x-18=0\\ \Rightarrow x^2-6x+3x-18=0\\ \Rightarrow x(x-6)+3(x-6)=0\end{array}$

  $\Rightarrow x+3=0$ and $x-6=0$

  $\Rightarrow x=-3$ and $x=6$

e

To determine

To calculate: The Value of xin the given expression i.e. $x^2-36=9x$

Answer to Problem 7PSA

Values of x are $-3$ and $12$ .

Explanation of Solution

Given information:$x^2-36=9x$

Calculation: $x^2-36=9x$

  $\begin{array}{l}\Rightarrow x^2-9x-36=0\\ \Rightarrow x^2-12x+3x-36=0\\ \Rightarrow x(x-12)+3(x-12)=0\end{array}$

  $\Rightarrow x+3=0$ and $x-12=0$

  $\Rightarrow x=-3$ and $x=12$

f

To determine

To calculate: The Value of xin the given expression i.e. $-x^2+5x+36=0$

Answer to Problem 7PSA

Values of x are $-4$ and $9$ .

Explanation of Solution

Given information:$-x^2+5x+36=0$

Calculation: $-x^2+5x+36=0$

  $\begin{array}{l}\Rightarrow -(x^2-5x-36)=0\\ \Rightarrow x^2-5x-36=0\\ \Rightarrow x^2-9x+4x-36=0\\ \Rightarrow x(x-9)+4(x-9)=0\end{array}$

  $\Rightarrow x+4=0$ and $x-9=0$

  $\Rightarrow x=-4$ and $x=9$