Complete the square to identify the two values that solve the following quadratic equation: x^2+8x=9 .
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
To complete the square and solve the quadratic equation x^2 + 8x = 9, follow these steps:
Step 1: Move the constant term (9) to the other side of the equation:
x^2 + 8x - 9 = 0
Step 2: Group the x terms together:
(x^2 + 8x) - 9 = 0
Step 3: To find the term that completes the square, take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:
(x^2 + 8x + 16) - 9 + 16 = 0 + 16
(x + 4)^2 - 9 + 16 = 16
Step 4: Simplify the equation:
(x + 4)^2 + 7 = 16
Step 5: Move the constant term (7) to the other side of the equation:
(x + 4)^2 = 16 - 7
(x + 4)^2 = 9
Step 6: Take the square root of both sides of the equation:
√((x + 4)^2) = ±√9
x + 4 = ±3
Step 7: Solve for x:
x = -4 + 3 or x = -4 - 3
x = -1 or x = -7
Therefore, the two values that solve the quadratic equation x^2 + 8x = 9 are x = -1 and x = -7.
To complete the square and solve the quadratic equation x^2 + 8x = 9, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 + 8x - 9 = 0
Step 2: To create a perfect square trinomial on the left side, take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 + 8x + (8/2)^2 = 9 + (8/2)^2
Simplifying this equation gives:
x^2 + 8x + 16 = 9 + 16
Step 3: Simplify further:
x^2 + 8x + 16 = 25
Step 4: Factor the left side:
(x + 4)(x + 4) = 25
Step 5: Take the square root of both sides:
(x + 4) = ±√25
Step 6: Solve for x by subtracting 4 from both sides:
x = -4 ± √25
Step 7: Simplify further:
x = -4 ± 5
So the two values that solve the quadratic equation x^2 + 8x = 9 are:
x = -4 + 5 = 1
and
x = -4 - 5 = -9
What is the asnwer
The two values that solve the quadratic equation x^2 + 8x = 9 are x = 1 and x = -9.
Using the quadratic formula, find the solution to x2+6x+9=0 .
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.
Solve −2x^2+3x−1=−2 using the quadratic formula. Round the solution(s) to the nearest hundredths. Enter the smaller solution first.
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.