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 Depdendent Variable

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 Dependent Variable

 Number of inequalities to solve: 23456789
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# Solving Quadratic Equations Using the Quadratic Formula

Example

Solve using the quadratic formula: 36x2 + 16 + 48x = 0

Solution

 Step 1 Write the quadratic equation in standard form, ax2 + bx + c = 0. 36x2 + 16 + 48x = 0 On the left side, write the terms in decreasing powers of x. Each term is divisible by 4. To simplify the calculations, divide both sides of the equation by 4. Step 2 Identify the values of a, b, and c. 36x2 + 16 + 48x = 0 Step 3 Substitute the values of a, b, and c into the quadratic formula. Step 4 Simplify. Step 5 Check each solution. We leave the check to you.

We say that is a solution of multiplicity two.

Example 2

Solve using the quadratic formula: x2 + 5 = 3x

 Step 1 Write the quadratic equation in standard form, ax2 + bx + c = 0. x2 + 5 = 3x Subtract 3x from both sides of the equation.Step 2 Identify the values of a, b, and c. Step 3 Substitute the values of a, b, and c into the quadratic formula. Step 4 Simplify. Notice the negative number under the square root symbol.

The radical does not represent a real number.

Therefore, the equation x2 + 5 = 3x has no real number solutions.

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