Solve the following quadratic equation using the quadratic formula.
−2x2−7x+13=0
−
2
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2
−
7
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+
13
=
0
**Note: Make sure to enter both solutions together in the space provided using the ±
±
symbol.
For example: x={12±10−−√}
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=
{
1
2
±
10
}
(If you need help with this, reach out to your teacher.)
(1 point)
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The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation -2x^2 - 7x + 13 = 0, we have a = -2, b = -7, and c = 13. Substituting these values into the quadratic formula, we get:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √(153)) / (-4)
Therefore, the solutions to the quadratic equation -2x^2 - 7x + 13 = 0 are:
x = (7 + √(153)) / (-4) and x = (7 - √(153)) / (-4)
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we can use the formula:
x = (-b ± √(b^2-4ac)) / (2a)
In this case, the values of a, b, and c are:
a = -2
b = -7
c = 13
Now, let's substitute these values into the formula:
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
Simplifying further:
x = (7 ± √(49 + 104)) / (-4)
x = (7 ± √(153)) / (-4)
Thus, the solutions to the quadratic equation −2x^2−7x+13=0 are:
x = (7 + √153) / -4
x = (7 - √153) / -4
Therefore, the solutions to the equation are x = (7 + √153) / -4 and x = (7 - √153) / -4.
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we can use the following steps:
Step 1: Identify the coefficients of the variables a, b, and c.
In this equation, a = -2, b = -7, and c = 13.
Step 2: Substitute the values of a, b, and c into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
Step 3: Calculate the discriminant (b^2 - 4ac):
Discriminant = (-7)^2 - 4(-2)(13)
Discriminant = 49 + 104
Discriminant = 153
Step 4: Substitute the discriminant value into the quadratic formula:
x = (-(-7) ± √(153)) / (2(-2))
x = (7 ± √(153)) / (-4)
Therefore, the solutions to the quadratic equation are:
x = (7 + √153) / (-4) and x = (7 - √153) / (-4)
Note: When writing the solutions together, we use the ± symbol.