Question

What are the solutions to the quadratic equation 3(x − 4)2 = 75?

Answer 1

Answer:

x=-1 and x=9

Step-by-step explanation:

$3(x-4)^{2} =75$

$(x-4)^{2} =\frac{75}{3}$

$(x-4)^{2}$=$25$

$(x-4)(x-4)$=$25$

$x^{2} -4x-4x+16$=$25$

$x^{2} -8x+16$=$25$

$x^{2} -8x+16-25=0$

$x^{2} -8x-9=0$

$(x-9)(x+1)=0$

$x-9=0\\x=0+9\\x=9$        $x+1=0\\x=0-1\\x=-1$

therefore x=9 and x=-1