WEBVTT
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Find the value of š¯‘¦ given that two š¯‘¦ minus 14 cubed minus 36 equals 28.
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Weā€™ll start with our equation two š¯‘¦ minus 14 cubed minus 36 equals 28.
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To solve for š¯‘¦, weā€™ll need to get it by itself.
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Weā€™ll need to isolate š¯‘¦.
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The first thing we can do is move the minus 36 to the other side of the equation.
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I can add 36 to both sides.
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Minus 36 plus 36 equals zero.
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28 plus 36 equals 64.
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Bring down the rest of our equation.
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Two š¯‘¦ minus 14 cubed equals 64.
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We now need to get rid of this cube.
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I can do that by taking two š¯‘¦ minus 14 cubed to the one-third power.
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And if I take the left side of the equation to the one-third power, Iā€™ll need to take the right side of the equation to the one-third power.
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When we raise a power to a power, we multiply them.
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And then it becomes two š¯‘¦ minus 14 to the three times one-third power is equal to.
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64 to the one-third power is the same thing as finding the cube root of 64.
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And that equals four.
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Four times four times four equals 64.
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Three times one-third equals one.
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And anything to the first power is itself.
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Weā€™ve now reduced our equation to say two š¯‘¦ minus 14 equals four.
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We can add 14 to the left and to the right.
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Minus 14 plus 14 equals zero.
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Four plus 14 equals 18.
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Bring down the rest of our equation.
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Two š¯‘¦ equals 18.
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Divide two š¯‘¦ by two, and divide 18 by two.
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Two š¯‘¦ divided by two equals š¯‘¦.
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Our twos cancel out.
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18 divided by two equals nine.
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The solution to the given equation is š¯‘¦ equals nine.