Find quadratic equation using the Quadratic Formula:

Solve the subsequent quadratic equation using the Quadratic Formula.

4x² + 2 = x² - 7x:

Solution:

Step 1. Write the equation in general forms.

4x² + 2 = x² -7x

3x² + 7x + 2 = 0

a= +3, b = +7, c = +2

Step 2.

x = (6 ± √20)/2

x = 3 ± 1/2√20

x = 3 ± √5

x = 3 + √5, 3 - √5

x = 3 + 2.236, 3 -2.236

x = 5.236, 0.746

Step 3. Check the roots.

2x² + 4 = 6x +x²

2(3 + √5)² +4 = 6(3 + √5) + (3+√5)²

2(9 + 6√5 + 5) + 4 = 18 +6√5 + 9 + 6√5 + 5

18 + 12√5 + 10 + 4 = 18 + 12√5 + 9 +5

32+ 12√5 = 32 + 12√5

And,

2x² + 4 = 6x + x²

2(3-√5)2 + 4 = 6(3- √5) + (3 - √5)2

2(9-6√5 + 5) + 4 = 18-6√5 + 9 -6√5 + 5

18 - 12√5 + 10 + 4 = 18 - 12√5 + 9 + 5

32- 12√5 = 32 - 12√5

Thus, the roots check.

The Quadratic Formula can be used to search the roots of any quadratic equation.   For a pure quadratic equation in that the numerical coefficient b equals zero, the Quadratic Formula (2-8) decreased to the formula given as Equation 9.

For b = 0, this decreases to the subsequent.