Question

Find the solutions of the quadratic equation –9x2 + 49 = 0.

Answer 1

x = 7/3

Explanation:

Given equation:

• –9x² + 49 = 0

To determine the value of "x", we need to isolate the x-variable and it's coefficient on one side of the equation. This can be done by subtracting 49 to both sides of the equation.

• ⇒ –9x² + 49 - 49 = 0 - 49
• ⇒ –9x² = -49

We can see that the negative sign in on both sides of the equation. Remove it by dividing -1 to both sides of the equation.

• ⇒ –9x² = -49
• ⇒ -9x²/-1 = -49/-1
• ⇒ 9x² = 49

Clearly, we can see that 9x² and 49 are perfect squares. Therefore,

• ⇒ 9x² = 49
• ⇒ (3x)² = (7)²

Take square root both sides of the equation:

• ⇒ √(3x)² = √(7)²
• ⇒ 3x = 7

To determine the value of "x", we need to isolate it "completely". This can be done by dividing 3 to both sides of the equation

• ⇒ 3x/3 = 7/3
• ⇒ x = 7/3

Therefore, the value of "x" must be 7/3.

Answer 2

x = 7∕3, –7∕3

Explanation:

To find the solutions of the quadratic equation -9x^2 + 49 = 0, we can solve for x by isolating x^2 first:

-9x^2 + 49 = 0

-9x^2 = -49

Dividing both sides by -9, we get:

x^2 = 49/9

Taking the square root of both sides, we get:

x = ± 7/3

Therefore, the solutions of the quadratic equation -9x^2 + 49 = 0 are x = 7/3 and x = -7/3.