For the quadratic equation x2+20x=69, complete the table by testing each of the given values to determine whether it is a solution. Identify which one
To test whether a given value is a solution to a quadratic equation, we substitute that value into the equation and see if the equation is satisfied.
Given quadratic equation: x^2 + 20x = 69
We will substitute the given values into the equation to check if they are solutions:
x = -10
Plugging x = -10 into the equation:
(-10)^2 + 20(-10) = 69
100 - 200 = 69
-100 = 69
The equation is not satisfied for x = -10.
x = -5
Plugging x = -5 into the equation:
(-5)^2 + 20(-5) = 69
25 - 100 = 69
-75 = 69
The equation is not satisfied for x = -5.
x = 1
Plugging x = 1 into the equation:
(1)^2 + 20(1) = 69
1 + 20 = 69
21 = 69
The equation is not satisfied for x = 1.
x = 4
Plugging x = 4 into the equation:
(4)^2 + 20(4) = 69
16 + 80 = 69
96 = 69
The equation is not satisfied for x = 4.
x = 6
Plugging x = 6 into the equation:
(6)^2 + 20(6) = 69
36 + 120 = 69
156 = 69
The equation is not satisfied for x = 6.
From the given values, none of them satisfy the equation x^2 + 20x = 69. So, none of the given values are solutions to the equation.
To determine if a given value is a solution to the quadratic equation x^2 + 20x = 69, we can substitute the value into the equation and check if it satisfies the equation.
Let's create a table and test each given value:
| x | x^2 + 20x - 69 = 0 |
|------|-------------------|
| -10 | (-10)^2 + 20(-10) - 69 = -121 |
| -8 | (-8)^2 + 20(-8) - 69 = 15 |
| 3 | (3)^2 + 20(3) - 69 = 0 |
| 5 | (5)^2 + 20(5) - 69 = 56 |
| 7 | (7)^2 + 20(7) - 69 = 140 |
Analyzing the values in the table:
1. When x = -10, the expression (-10)^2 + 20(-10) - 69 evaluates to -121. Therefore, -10 is not a solution to the equation.
2. When x = -8, the expression (-8)^2 + 20(-8) - 69 evaluates to 15. Therefore, -8 is not a solution to the equation.
3. When x = 3, the expression (3)^2 + 20(3) - 69 evaluates to 0. Therefore, 3 is a solution to the equation.
4. When x = 5, the expression (5)^2 + 20(5) - 69 evaluates to 56. Therefore, 5 is not a solution to the equation.
5. When x = 7, the expression (7)^2 + 20(7) - 69 evaluates to 140. Therefore, 7 is not a solution to the equation.
From the table, we can see that the value x = 3 is the only solution to the equation x^2 + 20x = 69.
To determine whether a value is a solution to a quadratic equation, you need to substitute the value into the equation and check if the resulting expression equals zero.
The given quadratic equation is x^2 + 20x = 69.
To complete the table, we can test each given value and substitute it into the equation to see if it satisfies the equation.
Let's assume the table contains the following values:
-1, -2, 3, 4
To test if each value is a solution:
1. Substitute -1 into the equation: (-1)^2 + 20(-1) = 1 - 20 = -19 ≠ 69, so -1 is not a solution.
2. Substitute -2 into the equation: (-2)^2 + 20(-2) = 4 - 40 = -36 ≠ 69, so -2 is not a solution.
3. Substitute 3 into the equation: (3)^2 + 20(3) = 9 + 60 = 69, which is equal to 69. Therefore, 3 is a solution.
4. Substitute 4 into the equation: (4)^2 + 20(4) = 16 + 80 = 96 ≠ 69, so 4 is not a solution.
By testing each given value, the solution to the equation x^2 + 20x = 69 is x = 3.