would you help me solve this quadratic equation

___________________

-4.51 - √4.51^2 + 4(16)(32.81)

____________________

2(-16)

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BRUCE S. | Learn & Master Physics & Math with Bruce SLearn & Master Physics & Math with Bruce...

QUADRATIC EQUATION FORM IS:

a*x^2 + b*x + c =0

IF YOU CAN'T FACOTOR THIS THEN USE THE FORMULA FOR x IS:

x = [ -b ±√{ b ^2 - 4*a*c } ] /2*a

BY INSPECTION:

b = -4.51

a = -16

c = 32.81

The original equation cannot be factored conveniently so use the formula to calculate x and remember there are 2 possible solutions because of the square root. I leave this to the stdent to calculate the x values.

If you are just after the original quadratic equation, it is:

-16*x^2 -4.51*x + 32.81 = 0

-4.51 - [(4.51)^{2} + 4(16)(32.81)]^{1/2}/2(-16) = [-4.51 + (6057.38)^{1/2}]/(-32) = (-4.51 + 77.8292)/(-32)

= 73.3192/(-32) = -2.29122

x = -b ± [b2 - 4ac]^{1/2}

2a

In this case b = 4.51, a = either 16 or -16 and c = 32.81

Hi L!

Once you have the values (a, b, and c from your quadratic equation) and have plugged them into the quadratic formula, as you did above, you can use a calculator to simplify the answer.

A few notes before you proceed:

*Make sure that when you do so, you have the first (-) sign that you wrote as a (±), meaning (+) or (-). That means that there will be two solutions to the problem: one that is computed by having that symbol as addition (+), and one that is computed with that symbol as subtraction (-). This is because a quadratic equation often crosses the x-axis at 2 points, because it is U-shaped.

*The meaning of the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)]/2a, is that two "solutions" (where the line passes through the x-axis, or x-intercept) are defined as (x,0) and (x,0). The quadratic formula gives you these two values for x. You find the two x values by calculating the value when the sign after (-b) is (+), and then when the sign after (-b) is (-).

*When using the calculator, just make sure to use parentheses to keep the expression consistent.

With a graphing calculator I would type: (-4.51 + √4.51^2 + 4(16)(32.81))/(2(-16)) for my first solution, and (-4.51 - √4.51^2 + 4(16)(32.81))/(2(-16)) for my second.

So, for this example, my first solution is x = -1.298 (approximately), and my solution can be written as a coordinate/x-intercept (-1.298, 0).

My second solution is x = 1.580 (approximately), and my solution can be written as a coordinate/x-intercept (1.581, 0).

This means that when graphed, the equation crosses the x-axis at these two points.

Hope this is helpful!

Hi L;

You have an equation in the form of...

x=[-b +/-(√b^{2}-4ac)]/2a

A quadratic equation is in the format of...

ax^{2}+bx+c=0

Let's begin with the denominator you provide...

2(-16)

a=-16

(-16)x^{2}+bx+c=0

This is consistent with the information within the square root...

√[4.51^2 + 4(16)(32.81)]

a is 16. However, 4ac is herewith added rather than subtracted. It is the negative number.

b is -4.51

c is 32.81

(-16)x^{2}-(4.51)x+32.81

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