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QUADRATIC EQUATION
STEPS USING THE QUADRATIC FORMULA



x2−4x−5=0

All equations of the form ax2+bx+c=0 can be solved using the quadratic formula: 2a−b±b2−4ac​​. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

x2−4x−5=0

This equation is in standard form: ax2+bx+c=0. Substitute 1 for a, −4 for b, and −5 for c in the quadratic formula, 2a−b±b2−4ac​​.

x=2−(−4)±(−4)2−4(−5)​​

Square −4.

x=2−(−4)±16−4(−5)​​

Multiply −4 times −5.

x=2−(−4)±16+20​​

Add 16 to 20.

x=2−(−4)±36​​

Take the square root of 36.

x=2−(−4)±6​

The opposite of −4 is 4.

x=24±6​

Now solve the equation x=24±6​ when ± is plus. Add 4 to 6.

x=210​

Divide 10 by 2.

x=5

Now solve the equation x=24±6​ when ± is minus. Subtract 6 from 4.

x=2−2​

Divide −2 by 2.

x=−1

The equation is now solved.

x=5x=−1

STEPS USING FACTORING BY GROUPING



x2−4x−5=0

To solve the equation, factor the left hand side by grouping. First, left hand side needs to be rewritten as x2+ax+bx−5. To find a and b, set up a system to be solved.

a+b=−4ab=1(−5)=−5

Since ab is negative, aand b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. The only such pair is the system solution.

a=−5b=1

Rewrite x2−4x−5 as (x2−5x)+(x−5).

(x2−5x)+(x−5)

Factor out x in x2−5x.

x(x−5)+x−5

Factor out common term x−5 by using distributive property.

(x−5)(x+1)

To find equation solutions, solve x−5=0 and x+1=0.

x=5x=−1

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Inequalities

The inequalities section of QuickMath allows you to solve virtually any inequality or system of inequalities in a single variable. In most cases, you can find exact solutions. Even when this is not possible, QuickMath may be able to give you approximate solutions to almost any level of accuracy you require. In addition, you can plot the regions satisfied by one or more inequalities in two variables, seeing clearly where the intersections of those regions occur.

What are inequalities?

Inequalities consist of two or more algebraic expressions joined by inequality symbols. The inequality symbols are :

greater than=greater than or equal to!= or not equal to

Here are a few examples of inequalities :

2 x - 9 > 0

x2 - 3 x + 5 0 AND x^2 - 5 < 0

13/9√5
Solution
13/9√5 × 9√5/9√5
117√5/81×5
=117√5/405

Any question

1/4(2x-2)≤1/2(1-x)
solution
1/4(2x-2)≤1/2(1-x)
multiply through by 4
4×¼(2x-2)≤4×½(1-x)
1(2x-2)≤2(1-x)
2x-2≤2-2x
collection of like terms
2x+2x≤2+2
4x≤4
divide through by 4
4x/4≤4/4
x≤1

Any question

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