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how to solve quadratic equation

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4 Answers

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 +/-(√b2-4ac)]/2a
A quadratic equation is in the format of...
ax2+bx+c=0
Let's begin with the denominator you provide...
2(-16)
a=-16
(-16)x2+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)x2-(4.51)x+32.81