Question

Complete the square to identify the two values that solve the following quadratic equation: x^2+8x=9 .
Answer
What is the asnwer
Answer
Using the quadratic formula, find the solution to x2+6x+9=0 .
Answer
Solve −2x^2+3x−1=−2 using the quadratic formula. Round the solution(s) to the nearest hundredths. Enter the smaller solution first.
Answer
How many real solutions does the following quadratic equation have? 25x^2+60x+36=0
Answered by GPT 3.5
To complete the square for the quadratic equation x^2+8x=9, we need to add and subtract the square of half the coefficient of x to both sides.

The coefficient of x is 8, so half of it is 4. The square of 4 is 16.

Adding and subtracting 16 in the equation, we get:

x^2 + 8x + 16 - 16 = 9

Rearranging the left side of the equation, we have:

(x^2 + 8x + 16) - 16 = 9

(x + 4)^2 - 16 = 9

(x + 4)^2 = 25

Taking the square root of both sides, we get:

x + 4 = ±√25

x + 4 = ±5

To isolate x, we subtract 4 from both sides:

x = -4 ± 5

The two values that solve the quadratic equation x^2+8x=9 are:

x = -4 + 5 = 1

x = -4 - 5 = -9
Answered by GPT 3.5
The two values that solve the quadratic equation x^2 + 8x = 9 are x = 1 and x = -9.
Answered by GPT 3.5
To find the solutions to the quadratic equation x^2 + 6x + 9 = 0 using the quadratic formula, we can use the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = 1, b = 6, and c = 9.

Plugging these values into the quadratic formula:

x = (-6 ± √(6^2 - 4(1)(9))) / 2(1)

Simplifying further:

x = (-6 ± √(36 - 36)) / 2

x = (-6 ± √(0)) / 2

Since the discriminant (b^2 - 4ac) is equal to 0, we get a repeated root.

x = -6 / 2

x = -3

Therefore, the solution to the quadratic equation x^2 + 6x + 9 = 0 is x = -3.
Answered by GPT 3.5
To solve the quadratic equation -2x^2 + 3x - 1 = -2 using the quadratic formula, we can use the formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this equation, a = -2, b = 3, and c = -1.

Plugging these values into the quadratic formula:

x = (-(3) ± √((3)^2 - 4(-2)(-1))) / 2(-2)

Simplifying further:

x = (-3 ± √(9 - 8)) / -4

x = (-3 ± √(1)) / -4

x = (-3 ± 1) / -4

This gives us two solutions:

x1 = (-3 + 1) / -4

x1 = -2 / -4

x1 = 1/2

x2 = (-3 - 1) / -4

x2 = -4 / -4

x2 = 1

Therefore, the solutions to the quadratic equation -2x^2 + 3x - 1 = -2, rounded to the nearest hundredth, are x = 0.50 and x = 1.
Answered by GPT 3.5
To determine the number of real solutions for the quadratic equation 25x^2 + 60x + 36 = 0, we can use the discriminant, which is given by the formula: b^2 - 4ac.

In this equation, a = 25, b = 60, and c = 36.

Calculating the discriminant:

Discriminant = (60)^2 - 4(25)(36)
Discriminant = 3600 - 3600
Discriminant = 0

Since the discriminant is equal to zero, there is only one real solution.