Solve Using the Quadratic Formula x^2-15=0

Solve Using the Quadratic Formula x^2-15=0

To solve the equation x² – 15 = 0 using the quadratic formula, we identify ‘a’ as 1, ‘b’ as 0, and ‘c’ as -15. Plugging these values into the formula, we find two solutions: x = √15 and x = -√15. These are the values that satisfy the equation and make it equal to zero.

To solve the quadratic equation x^2 – 15 = 0 using the quadratic formula, we first need to identify the coefficients of the equation. In this case, the coefficients are:

a = 1 (coefficient of x^2) b = 0 (there is no x-term, so the coefficient is 0) c = -15 (constant term)

Now, we can use the quadratic formula to find the solutions for x:

x = (-b ± √(b² – 4ac)) / (2a)

Substituting the values of a, b, and c into the formula:

x = (0 ± √(0² – 4(1)(-15))) / (2(1))

x = (± √(0 + 60)) / 2

x = (± √60) / 2

Now, we can simplify √60:

√60 = √(4 * 15) = 2√15

So, the solutions for x are:

x₁ = (2√15) / 2 = √15 x₂ = -(2√15) / 2 = -√15

Now, let’s create a table to show the solutions:

x	Solution
x₁	√15
x₂	-√15

These are the two solutions to the equation x^2 – 15 = 0.

Using the Quadratic Formula

The quadratic formula provides a straightforward way to solve any quadratic equation in the form ax2 + bx + c = 0. Let’s apply the quadratic formula step-by-step to solve the equation x2 – 15 = 0.

Write the Equation in Standard Form

The quadratic formula works when the equation is written in standard form ax2 + bx + c = 0.

Our equation x2 – 15 = 0 can be rewritten in standard form as:

1×2 + 0x – 15 = 0

Where a = 1, b = 0, and c = -15.

Apply the Quadratic Formula

The quadratic formula is:

x = (-b ± √(b2 – 4ac)) / 2a

Plugging in the values a = 1, b = 0, and c = -15 gives us:

x = (0 ± √(02 – 4(1)(-15))) / 2(1)

Simplify Inside the Square Root

Simplifying inside the square root:

x = (0 ± √(0 + 60)) / 2 x = (0 ± √60) / 2

Take the Square Root

√60 = ±8 since the square root of 60 is 8.

Solve

x = (0 ± 8) / 2 x = +/-4

Therefore, the solutions are x = -4 and x = 4.

The quadratic formula allows you to systematically solve any quadratic equation. By plugging in the equation’s values and simplifying, you can easily determine the roots. With practice, use of the quadratic formula becomes second nature for unlocking the solutions to quadratics.