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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.
Next, substitute in the `-` portion of the `+-` to find the second solution.
The complete solution is the result of both the `+` and `-` portions of the solution.
Solve `3x^(2) + 1 = -26`
`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.
To bring 26 on LHS we have to add 26 to both sides;
Take 3 common:-
Divide by 3 both sides:-
Subtract 9 on both sides;
Taking square root on both sides;
The square root and the exponent will be canceled with each other, then we will get;
Now as `sqrt(-1)=i` `hence; `
Hence the answer is 3i.
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.
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:
= `(+-6*sqrt (-1))/2`
sqrt both sides
x= sqrt -9
seperate into sqrt-1*sqrt9
sqrt -1 is i
and sqrt9= 3
3i is the answer.
divide by 3
`(3x^2) / 3 = (-27) / 3`
find the square root
-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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