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Q. 1

Expert-verifiedFound in: Page 315

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

Solve $\text{}{x}^{2}-7x-30=0\text{.}$

The solution of the given equation is and $x=-3andx=10.$

The given equation is $\text{}{x}^{2}-7x-30=0\text{}$

We have to find the solution of the equation i.e the value of $x$ that satisfies the given equation.

$\begin{array}{l}\text{The given equation is}{x}^{2}-7x-30=0.\\ \Rightarrow {x}^{2}-7x-30=0\\ \Rightarrow {x}^{2}+3x-10x-30=0\text{}\left[\text{Split the middle term}\right]\\ \Rightarrow x\left(x+3\right)-10\left(x+3\right)=0\text{}\left[\text{Take out the common terms}\right]\\ \Rightarrow \left(x-10\right)\left(x+3\right)=0\text{}\left[\text{Form the factors}\right]\end{array}$

$\begin{array}{l}\text{By zero product rule,}\\ \Rightarrow x-10=0\\ \Rightarrow x=10\\ \text{and,}\\ \Rightarrow x+3=0\\ \Rightarrow x=-3\\ \text{The solution set is}\left\{-3,10\right\}\end{array}$

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