Question

Questlon 12 of 25
Find the solutions to 9x2 - 63x= 0.

Answer 1

Answer 2/7

Explaination
multiply the numbers
9x2-63x=0
18 - 63x= 0
Move the constant to the right

-63x = -18
Divide both sides by -63
2/7

Answer 2

x =0 ,x =7

Explanation:

Method 1 ; Factoring

`9x^2 -63x =0\\\\\mathrm{Solve\:by\:factoring}\\\mathrm{Factor\:}9x^2-63x:\quad 9x\left(x-7\right)\\\\9x\left(x-7\right)=0\\\\\mathrm{Using\:the\:Zero\:Factor\:Principle:}\\if\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)\\\\x =0\\\mathrm{Solve\:}\:x-7=0:\quad x=7\\x=0,\:x=7`

Method 2 ; Completing the square

`9x^2-63x=0\\\\\mathrm{Divide\:both\:sides\:by\:}9\\(9x^2-63x)/(9)=(0)/(9)\\\\x^2-7x=0\\\mathrm{Solve\:by\:completing\:the\:square}\\\mathrm{Write\:equation\:in\:the\:form:\:\:}\\x^2+2ax+a^2=\left(x+a\right)^2\\\\\mathrm{Solve\:for\:}a,\:2ax=-7x:\quad a=-(7)/(2)\\\\\mathrm{Add\:}a^2=\left(-(7)/(2)\right)^2\mathrm{\:to\:both\:sides}\\x^2-7x+\left(-(7)/(2)\right)^2=0+\left(-(7)/(2)\right)^2\\\\\mathrm{Simplify\:}\\0+\left(-(7)/(2)\right)^2:\quad (49)/(4)`

`x^2-7x+\left(-(7)/(2)\right)^2=(49)/(4)\\\\\mathrm{Complete\:the\:square}\\\left(x-(7)/(2)\right)^2=(49)/(4)\\\\\mathrm{For\:}f^2\left(x\right)=a\mathrm{\:the\:solutions\:are\:}f\left(x\right)=√(a),\:-√(a)\\\\\mathrm{Solve\:}\:x-(7)/(2)=\sqrt{(49)/(4)}:\quad x=7\\\\\mathrm{Solve\:}\:x-(7)/(2)=-\sqrt{(49)/(4)}:\quad x=0\\\\x=7,\:x=0`