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erma4kov [3.2K]
3 years ago
10

Which equation shows the quadratic formula used correctly to solve 7x2 = 9 + x for x?

Mathematics
2 answers:
nydimaria [60]3 years ago
7 0
I hope this helps you

otez555 [7]3 years ago
5 0

Answer:

Quadratic formula for given equation is x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}

Step-by-step explanation:

Given Quadratic Equation is  7x² = 9 + x

We need to find correct Quadratic formula for the given quadratic equation.

If the quadratic equation is in standard for,

ax² + bx + c = 0

then quadratic formula is given by,

x=\frac{-b\pm\sqrt{b-4ac}}{2a}

First we rewrite the quadratic equation,

7x² - x - 9 = 0

by comparing with standard form of equation we get,

a = 7  ,   b = -1  and c = -9

oNw putting these value in quadratic formula we get,

x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}

Therefore, Quadratic formula for given equation is x=\frac{-(-1)\pm\sqrt{(-1)-4(7)(-9)}}{2\times7}

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Given a rectangle with length of (2x+9)cm and width of (3x+1)cm.Two squares, each with sides x cm is removed from the rectangle.
il63 [147K]

Answer: The length is 13cm and the width is 7cm

Step-by-step explanation:

For a rectangle of length L and width W, the area is:

A = W*L

In this case we have:

L = (2*x + 9) cm

W=(3*x + 1) cm

Then the area of the rectangle is:

A = (2*x + 9)*(3*x + 1) cm^2

A = (6*x^2 + 2*x + 27*x + 9) cm^2

A = (6*x^2 + 29*x + 9) cm^2

now we remove two squares with sides of x cm

The area of each one of these squares is (x cm)*(x cm)  = x^2 cm^2

Then the area of the figure will be:

area = (6*x^2 + 29*x + 9) cm^2 - (2*x^2 ) cm^2

area = (4*x^2 + 29*x + 9) cm^2

Now we know that the area of this shape is 83 cm^2, then we need to solve:

83 cm^2 = (4*x^2 + 29*x + 9) cm^2

0 =  (4*x^2 + 29*x + 9) cm^2 - 83 cm^2

0 = (4*x^2 + 29*x - 74) cm^2

Then we need to solve:

0 = 4*x^2 + 29*x - 74

Here we can use Bhaskara's equation, the solutions of this equation are given by:

x = \frac{-29 \pm \sqrt{29^2 - 4*4*(-74)}  }{2*4} = \frac{-29 \pm 45}{8}

Then the two solutions are:

x = (-29 - 45)/8 = -9.25  (for how the length and width are defined, we can not have x as a negative number, then this solution can be discarded).

The other solution is:

x = (-29 + 45)/8 = 2

x = 2

Then the length and width of the rectangle are:

Length = (2*2 + 9)cm = 13 cm

Width = (3*2 + 1)cm = 7cm

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Step-by-step explanation:

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