Question

Solve the equation by completing the square. Round to the nearest hundredth if necessary. x^2 + 3x - 5= 0

Answer 1

`\large\boxed{x\approx-4.19\ \vee\ x\approx1.19}`

Explanation:

`x^2+3x-5=0\qquad\text{add 5 to both sides}\\\\x^2+3x=5\\\\x^2+2(x)(1.5)=5\qquad\text{add}\ 1.5^2=2.25\ \text{to both sides}\\\\x^2+2(x)(1.5)+1.5^2=5+2.25\qquad\text{use}\ (a+b)^2=a^2+2ab+b^2\\\\(x+1.5)^2=7.25\Rightarrow x+1.5=\pm√(7.25)\\\\x+1.5\approx\pm2.69\\\\x+1.5\approx-2.69\ \vee\ x+1.5\approx2.69\qquad\text{subtract 1.5 from both sides}\\\\x\approx-4.19\ \vee\ x\approx1.19`