solve 3x2+1=-26

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kingattaskus12's profile pic

kingattaskus12 | (Level 3) Adjunct Educator

Posted on

Since 1 does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting `1` from both sides.

`3x^2 = - 1 - 26`


Subtract 26 from `-1` to get `-27` .

`3x^2 = - 27`


Divide each term in the equation by `3` .

`(3x^2)/3 = -27/3`


Simplify the left-hand side of the equation by canceling the common factors.

`x^2 = - 27/3`


Simplify the equation.

`x^2 = - 9`


Take the square root of both sides of the equation to eliminate the exponent on the left-hand side.

`x = +- sqrt(-9)`


Pull all perfect square roots out from under the radical. In this case, remove the `3i` because it is a perfect square.

`x = +- 3 i`


First, substitute in the `+` portion of the `+-` to find the first solution.

`x=3i `


Next, substitute in the `-` portion of the `+-` to find the second solution.

`x=-3i `


The complete solution is the result of both the `+` and `-` portions of the solution.

`x=3i,-3i`

baxthum8's profile pic

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

Solve `3x^(2) + 1 = -26`

Subtract 1.

`3x^(2) = -27`

Divide by 3.

`x^2 = -9`

Take square root of each side.

`x =sqrt(-9) = ` No real solution, as you cna't take the square root of a negative number.

As a complex number, `sqrt(-9) =sqrt(-1)*sqrt(9)`

Since `sqrt(-1) = i`  , this gives the complex number `3i.`

As a real solution, there is not one.  As a complex number the solution is 3i.

sid-sarfraz's profile pic

sid-sarfraz | Student, Graduate | (Level 2) Salutatorian

Posted on

QUESTION:-

solve

3x2+1=-26

SOLUTION:-

`3x^2+1=-26`

To bring 26 on LHS we have to add 26 to both sides;

`3x^2+1+26=-26+26`

`3x^2+1+26=0`

`3x^2+27=0`

Take 3 common:-

`3(x^2+9)=0`

Divide by 3 both sides:-

`(3(x^2+9))/3=0/3`

`x^2+9=0`

Subtract 9 on both sides;

`x^2+9-9=0-9`

`x^2=-9`

Taking square root on both sides;

`sqrt(x^2)=sqrt(-9)`

The square root and the exponent will be canceled with each other, then we will get;

`x=sqrt(-9)`

`x=sqrt(3*3*(-1))`

Now as `sqrt(-1)=i` `hence; `

`x=3i`

Hence the answer is 3i.

` `

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

Posted on

3x^2 + 1 = -26

In order to simplify this our main purpose is to isolate x, which can be done as follows,

3x^2 + 1 - 1 = -26 - 1          Subtract 1 from both sides

3x^2 = -27

3x^2/3 = -27/3                    Divide both sides by 3

x^2 = -9 

Taking square root on both sides

x = `sqrt(-9)`

x = 3i Answer. 

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

To solve the equation 3x^2+1=-26 use the quadratic formula.

The solution of the quadratic equation ax^2 + bx + c = 0 is ` (-b+-sqrt(b^2 - 4ac))/(2a)`

3x^2 + 1 = -26

3x^2 + 27 = 0

3*(x^2 + 9) = 0

x^2 + 9 = 0

Here, a = 1, b = 0 and c = 9

The solution of the equation is:

`(+-sqrt(-36))/2`

= `(+-6*sqrt (-1))/2`

= `+-3i`

acompanioninthetardis's profile pic

acompanioninthetardis | Student, Undergraduate | (Level 1) Valedictorian

Posted on

3x2+1=-26

subtract 1

3X2=-27

3x^2=-27

x^2=-9

sqrt both sides

x= sqrt -9

seperate into sqrt-1*sqrt9

sqrt -1 is i

and sqrt9= 3

3i is the answer. 

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

`3x^2+1=-26`

`3x^2=-27`

divide by 3

`(3x^2) / 3 = (-27) / 3`

`x^2= -9`

find the square root

`sqrt(x^2)=sqrt(-9)`

`x=+- sqrt(-3)`

-3 is an imaginary number so this problem doesn't have a real solution:

but the complex solutions would be: `-3i ` and `3i`

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