Solved on Nov 10, 2023

Solve $-6 x^{\frac{3}{2}}+5=-2,053$ for $x$ . Options: A) $x=49$ , B) $x=28$ , C) $x=14$ , D) $x=7$ .

STEP 1

Assumptions1. The equation is $-6 x^{\frac{3}{}}+5=-,053$ . We are solving for $x$

STEP 2

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting5 from both sides of the equation.
$-6 x^{\frac{}{2}}+5-5=-2,053-5$

STEP 3

implify the equation.
$-6 x^{\frac{3}{2}}=-2,058$

STEP 4

Next, we need to get rid of the coefficient of $x$ term which is -6. We can do this by dividing both sides of the equation by -6.
$\frac{-6 x^{\frac{3}{2}}}{-6}=\frac{-2,058}{-6}$

STEP 5

implify the equation.
$x^{\frac{3}{2}}=343$

STEP 6

To solve for $x$ , we need to get rid of the exponent $\frac{3}{2}$ . We can do this by raising both sides of the equation to the power of $\frac{2}{3}$ .
$(x^{\frac{3}{2}})^{\frac{2}{3}}=(343)^{\frac{2}{3}}$

STEP 7

implify the equation.
$x=(343)^{\frac{2}{3}}$

STEP 8

Calculate the value of $x$ .
$x=7^2=49$ So, $x=49$ .

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Solve $-6 x^{\frac{3}{2}}+5=-2,053$ for $x$ . Options: A) $x=49$ , B) $x=28$ , C) $x=14$ , D) $x=7$ .

STEP 1

Assumptions1. The equation is $-6 x^{\frac{3}{}}+5=-,053$ . We are solving for $x$

STEP 2

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting5 from both sides of the equation.
$-6 x^{\frac{}{2}}+5-5=-2,053-5$

STEP 3

implify the equation.
$-6 x^{\frac{3}{2}}=-2,058$

STEP 4

Next, we need to get rid of the coefficient of $x$ term which is -6. We can do this by dividing both sides of the equation by -6.
$\frac{-6 x^{\frac{3}{2}}}{-6}=\frac{-2,058}{-6}$

STEP 5

implify the equation.
$x^{\frac{3}{2}}=343$

STEP 6

To solve for $x$ , we need to get rid of the exponent $\frac{3}{2}$ . We can do this by raising both sides of the equation to the power of $\frac{2}{3}$ .
$(x^{\frac{3}{2}})^{\frac{2}{3}}=(343)^{\frac{2}{3}}$

STEP 7

implify the equation.
$x=(343)^{\frac{2}{3}}$

STEP 8

Calculate the value of $x$ .
$x=7^2=49$ So, $x=49$ .

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Solve −6x32+5=−2,053-6 x^{\frac{3}{2}}+5=-2,053−6x23​+5=−2,053 for xxx. Options: A) x=49x=49x=49, B) x=28x=28x=28, C) x=14x=14x=14, D) x=7x=7x=7.

STEP 1

Assumptions1. The equation is −6x3+5=−,053-6 x^{\frac{3}{}}+5=-,053−6x3​+5=−,053 . We are solving for xxx

STEP 2

First, we need to isolate the term with xxx on one side of the equation. We can do this by subtracting5 from both sides of the equation.−6x2+5−5=−2,053−5-6 x^{\frac{}{2}}+5-5=-2,053-5−6x2​+5−5=−2,053−5

STEP 3

implify the equation.−6x32=−2,058-6 x^{\frac{3}{2}}=-2,058−6x23​=−2,058

STEP 4

Next, we need to get rid of the coefficient of xxx term which is -6. We can do this by dividing both sides of the equation by -6.−6x32−6=−2,058−6\frac{-6 x^{\frac{3}{2}}}{-6}=\frac{-2,058}{-6}−6−6x23​​=−6−2,058​

STEP 5

implify the equation.x32=343x^{\frac{3}{2}}=343x23​=343

STEP 6

To solve for xxx, we need to get rid of the exponent 32\frac{3}{2}23​. We can do this by raising both sides of the equation to the power of 23\frac{2}{3}32​.(x32)23=(343)23(x^{\frac{3}{2}})^{\frac{2}{3}}=(343)^{\frac{2}{3}}(x23​)32​=(343)32​

STEP 7

implify the equation.x=(343)23x=(343)^{\frac{2}{3}}x=(343)32​

STEP 8

Calculate the value of xxx.x=72=49x=7^2=49x=72=49So, x=49x=49x=49.

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Solve $-6 x^{\frac{3}{2}}+5=-2,053$ for $x$ . Options: A) $x=49$ , B) $x=28$ , C) $x=14$ , D) $x=7$ .

Assumptions1. The equation is $-6 x^{\frac{3}{}}+5=-,053$ . We are solving for $x$

First, we need to isolate the term with $x$ on one side of the equation. We can do this by subtracting5 from both sides of the equation.
$-6 x^{\frac{}{2}}+5-5=-2,053-5$

implify the equation.
$-6 x^{\frac{3}{2}}=-2,058$

Next, we need to get rid of the coefficient of $x$ term which is -6. We can do this by dividing both sides of the equation by -6.
$\frac{-6 x^{\frac{3}{2}}}{-6}=\frac{-2,058}{-6}$

implify the equation.
$x^{\frac{3}{2}}=343$

To solve for $x$ , we need to get rid of the exponent $\frac{3}{2}$ . We can do this by raising both sides of the equation to the power of $\frac{2}{3}$ .
$(x^{\frac{3}{2}})^{\frac{2}{3}}=(343)^{\frac{2}{3}}$

implify the equation.
$x=(343)^{\frac{2}{3}}$

Calculate the value of $x$ .
$x=7^2=49$ So, $x=49$ .