QuestionSolve the equation $5 x^{2}-x-7=0$ . It cannot be factored.

Studdy Solution

STEP 1

Assumptions1. The given equation is a quadratic equation of the form $ax^{}+bx+c=0$ . . The coefficients a, b, and c are5, -1, and -7 respectively.
3. The quadratic formula is used to solve the equation, which is $x=\frac{-b\pm\sqrt{b^{}-4ac}}{a}$ .

STEP 2

First, identify the coefficients a, b, and c from the given quadratic equation.
$a=5, b=-1, c=-7$

STEP 3

Now, plug in the values of a, b, and c into the quadratic formula.
$x=\frac{-(-1)\pm\sqrt{(-1)^{2}-5(-7)}}{2*5}$

STEP 4

implify the expression inside the square root.
$x=\frac{1\pm\sqrt{1+140}}{10}$

STEP 5

Calculate the value inside the square root.
$x=\frac{1\pm\sqrt{141}}{10}$

STEP 6

Now, calculate the two possible values for x by using the plus and minus in the formula.
$x_{1}=\frac{1+\sqrt{141}}{10}, x_{2}=\frac{1-\sqrt{141}}{10}$ The solutions to the equation $5x^{2}-x-=0$ are $x_{1}=\frac{1+\sqrt{141}}{10}$ and $x_{2}=\frac{1-\sqrt{141}}{10}$ .

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