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Solve for [tex]x[/tex]:
[tex]\[2x^2 - 3 = 15\][/tex]

Sagot :

GinnyAnsweridn
Let's solve the equation [tex]\( 2x^2 - 3 = 15 \)[/tex] step-by-step.

1. Start with the given equation:
[tex]\[ 2x^2 - 3 = 15 \][/tex]

2. Isolate the term with the variable:
Add 3 to both sides of the equation to move the constant term to the right side:
[tex]\[ 2x^2 - 3 + 3 = 15 + 3 \][/tex]
Simplifying both sides, we get:
[tex]\[ 2x^2 = 18 \][/tex]

3. Solve for [tex]\( x^2 \)[/tex]:
Divide both sides of the equation by 2 to isolate [tex]\( x^2 \)[/tex]:
[tex]\[ \frac{2x^2}{2} = \frac{18}{2} \][/tex]
Simplifying, we obtain:
[tex]\[ x^2 = 9 \][/tex]

4. Solve for [tex]\( x \)[/tex]:
To remove the square, take the square root of both sides of the equation. Remember that the square root can yield both positive and negative results:
[tex]\[ x = \pm \sqrt{9} \][/tex]

5. Simplify the square root:
Since the square root of 9 is 3, we have:
[tex]\[ x = \pm 3 \][/tex]

Therefore, the solutions to the equation [tex]\( 2x^2 - 3 = 15 \)[/tex] are:
[tex]\[ x = 3 \quad \text{and} \quad x = -3 \][/tex]
Wegnerkolmp2741oidn

Answer:

x = ±3

Step-by-step explanation:

Solve for x:

2x^2 - 3 = 15

Add 3 to each side:

2x^2 - 3+3 = 15+3

2x^2 = 18

Divide each side by 2:

2x^2 /2 = 18/2

x^2 = 9

Take the square root of each side:

[tex]\sqrt{x^2}[/tex] = [tex]\sqrt{9}[/tex]

x = ±3

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