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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Quadratic Equations by Factoring

Example

Solve by factoring: 25 + 30x = -9x2

Solution

 Step 1 Write the equation in the form ax2 + bx + c = 0Add 9x2 to both sides. Step 2 Factor the polynomial. The first and last terms of the trinomial are perfect squares. The middle term, 30x, is 2(3x)(5). Since the trinomial has the form a2 + 2ab + b2, it is a perfect 9x2 + 30x + 25  (3x)2 + 30x + (5)2 (3x)2 + 2(3x)(5) + (5)2 = 0 = 0= 0 A perfect square trinomial can be written as the product of two identical binomials. (3x + 5)(3x + 5) = 0 Step 3 Use the Zero Product Property. 3x + 5 = 0 or 3x + 5 = 0 Step 4 Solve the resulting equations. Step 5 Check each answer. We leave the check to you.

So, 25 + 30x = -9x2 has two equal solutions,

Every quadratic equation has two solutions. In the previous example, the two solutions are the same, . We call a solution of multiplicity two.