Answer
$t = -\frac{45}{2}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {-2(-\frac{45}{2}) + 4} = 7$
Multiply to simplify:
$\sqrt {45 + 4} = 7$
Evaluate what is inside the radical:
$\sqrt {49} = 7$
Evaluate the square root:
$7 = 7$
Work Step by Step
We need to get rid of the radical, so we square both sides of the equation:
$-2t + 4 = 7^{2}$
Evaluate the right side of the equation:
$-2t + 4 = 49$
Subtract $4$ from both sides of the equation to collect constants on the right side of the equation:
$-2t = 45$
Divide both sides by $-2$ to solve for $t$:
$t = -\frac{45}{2}$
To check if our solution is correct, we plug it into the original equation:
$\sqrt {-2(-\frac{45}{2}) + 4} = 7$
Multiply to simplify:
$\sqrt {45 + 4} = 7$
Evaluate what is inside the radical:
$\sqrt {49} = 7$
Evaluate the square root:
$7 = 7$
