Video: Finding the Value of a Variable in a Cubic Equation

Find the value of 𝑦 given that (2𝑦 − 14)³ − 36 = 28.

02:30

Video Transcript

Find the value of 𝑦 given that two 𝑦 minus 14 cubed minus 36 equals 28.

We’ll start with our equation two 𝑦 minus 14 cubed minus 36 equals 28. To solve for 𝑦, we’ll need to get it by itself. We’ll need to isolate 𝑦. The first thing we can do is move the minus 36 to the other side of the equation. I can add 36 to both sides. Minus 36 plus 36 equals zero. 28 plus 36 equals 64. Bring down the rest of our equation. Two 𝑦 minus 14 cubed equals 64.

We now need to get rid of this cube. I can do that by taking two 𝑦 minus 14 cubed to the one-third power. And if I take the left side of the equation to the one-third power, I’ll need to take the right side of the equation to the one-third power. When we raise a power to a power, we multiply them. And then it becomes two 𝑦 minus 14 to the three times one-third power is equal to. 64 to the one-third power is the same thing as finding the cube root of 64. And that equals four. Four times four times four equals 64. Three times one-third equals one. And anything to the first power is itself.

We’ve now reduced our equation to say two 𝑦 minus 14 equals four. We can add 14 to the left and to the right. Minus 14 plus 14 equals zero. Four plus 14 equals 18. Bring down the rest of our equation. Two 𝑦 equals 18. Divide two 𝑦 by two, and divide 18 by two. Two 𝑦 divided by two equals 𝑦. Our twos cancel out. 18 divided by two equals nine. The solution to the given equation is 𝑦 equals nine.

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