Question

-×^2 - 7x + 7 = -2x^2 to the nearest tenth.

Answer 1

Solving Quadratic Equations

The general form of a quadratic equation is:

`ax^2+bx+c=0`

It can be solved by using the formula:

`x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

we have the following equation:

`-x^2-7x+7=-2x^2`

we need to put this equation in standard form as explained above

Adding 2x^2:

`\begin{gathered} 2x^2-x^2-7x+7=-2x^2+2x^2 \\ \text{Simplifying:} \\ x^2-7x+7=0 \end{gathered}`

Now we have the equation in the correct form, we find the value of the variables as follows:

a=1, b=-7, c=7

Applying the formula:

`x=\frac{-(-7)\pm\sqrt[]{(-7)^2-4(1)(7)}}{2(1)}`

Operating:

`x=\frac{7\pm\sqrt[]{49-28}}{2}=\frac{7\pm\sqrt[]{21}}{2}`

The square root of 21 is not exact, we use two decimals so far, and we'll round to one decimal at the very last time.

Taking the square root:

`\begin{gathered} x=(7\pm4.58)/(2) \\ We\text{ have two solutions:} \\ x=(7+4.58)/(2)=7.79 \\ x=(7-4.58)/(2)=1.21 \end{gathered}`

The solutions (to the nearest tenth) are:

x= 7.8

x=1.2

Answer complete

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