How do you solve the equation $4+sqrt(4t-4)=t$ ?

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Answer 1 · 2016-10-17T06:22:48

$t=2$ or $t=10$

$4+ sqrt(4t-4)= t$

Subtract 4 from both sides.

$sqrt(4t-4)= t-4$

Square both sides.

$4t-4 = (t-4)^2$

Expand the right side.

$4t-4= (t-4)(t-4)$

$4t-4= t(t-4)-4(t-4)$

$4t-4=t^2-4t-4t+16$ (since multiplying two negatives produces a positive)

Simplify the equation on the right.

$4t-4=t^2-8t+16$

Subtract $(4t-4)$ from both sides.

$0=t^2-12t+20$ or $t^2 -12t+20=0$

Factorise the equation.

$t^2-2t-10t+20=0$

$t(t-2)-10(t-2)=0$

$(t-2)(t-10)=0$

$:. t=2$ or $t=10$

How do you solve the equation 4+sqrt(4t-4)=t4+sqrt(4t-4)=t?