Solve the following quadratic equation using the quadratic formula. −2x2−7x+13=0 **Note: Make sure to enter both solutions together in the space provided using the ± symbol. For example: x={12±10−−√} (If you need help with this, reach out to your teacher.) (1 point)
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, c = 13
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
Simplifying further:
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)
x = (7 - √(153)) / (-4)
So the final answer is:
x = (7 + √(153)) / (-4), (7 - √(153)) / (-4)
To solve the quadratic equation −2x^2−7x+13=0 using the quadratic formula, we need to identify the coefficients a, b, and c from the equation.
In this equation, a = -2, b = -7, and c = 13.
The quadratic formula is given by:
x = (-b ± √(b^2-4ac))/(2a)
Substituting the values into the 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 are:
x = (7 + √(153))/(4)
x = (7 - √(153))/(4)
So, the solutions together are:
x = (7 + √(153))/(4) or x = (7 - √(153))/(4)
To solve the quadratic equation −2x^2 − 7x + 13 = 0 using the quadratic formula, follow these steps:
Step 1: Identify the coefficients. In this equation, the coefficient of x^2 is -2, the coefficient of x is -7, and the constant term (no x) is 13.
Step 2: Recall the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation.
Step 3: Substitute the values into the quadratic formula. In this case, a = -2, b = -7, and c = 13.
x = (-(-7) ± √((-7)^2 - 4(-2)(13))) / (2(-2))
= (7 ± √(49 + 104)) / (-4)
= (7 ± √153) / (-4)
Step 4: Simplify the equation to obtain the final answer.
x = (7 + √153) / (-4) and x = (7 - √153) / (-4)
Hence, the solutions to the quadratic equation −2x^2 − 7x + 13 = 0 using the quadratic formula are:
x = (7 + √153) / (-4) and x = (7 - √153) / (-4)