SOLUTION: what are the solutions of 4x2-21x-18=0

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Question 828414: what are the solutions of 4x2-21x-18=0
Found 3 solutions by TimothyLamb, LinnW, MathTherapy:
Answer by TimothyLamb(4379) About Me  (Show Source):
You can put this solution on YOUR website!
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4x^2 - 21x - 18 =0
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the above quadratic equation is in standard form, with a=4, b=-21, and c=-18
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
4 -21 -18
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic has two real roots at:
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x = 6
x = -0.75
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php

Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
4x%5E2-21x-18=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-21x%2B-18+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-21%29%5E2-4%2A4%2A-18=729.

Discriminant d=729 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--21%2B-sqrt%28+729+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-21%29%2Bsqrt%28+729+%29%29%2F2%5C4+=+6
x%5B2%5D+=+%28-%28-21%29-sqrt%28+729+%29%29%2F2%5C4+=+-0.75

Quadratic expression 4x%5E2%2B-21x%2B-18 can be factored:
4x%5E2%2B-21x%2B-18+=+4%28x-6%29%2A%28x--0.75%29
Again, the answer is: 6, -0.75. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-21%2Ax%2B-18+%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

what are the solutions of 4x2-21x-18=0


4x%5E2+-+21x+-+18+=+0



Factors of - 72 (a * c) that sum to - 21 (b) are: - 24 and + 3

Thus, we have: 4x%5E2+-+24x+%2B+3x+-+18+=+0

4x%28x+-+6%29+%2B+3%28x+-+6+%29+=+0

%284x+%2B+3%29%28x+-+6%29+=+0

4x + 3 = 0        OR        x - 6 = 0

4x = 0 - 3        OR        x = 0 + 6

  highlight_green%28x+=+-+3%2F4%29         OR        highlight_green%28x+=+6%29

You can do the check!! 



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