Question

Use graphing technology to approximate the solutions of x² – 5x + 3 = 2x - 5 to the nearest tenth

A) x = 4.2
B) x = 1.8
C) x = 0.5
D) x = 7.2

Answer 1

The equation x² - 5x + 3 = 2x - 5 is first transformed into the standard quadratic form, x² - 7x + 8 = 0, then solved using the quadratic formula. The values found are then approximated to the nearest tenth, which can be verified using graphing technology.

Step-by-step explanation:

To approximate the solutions to the equation x² – 5x + 3 = 2x - 5, first we need to rearrange it into a standard quadratic form which equals zero:

Combining like terms, we get:

x² - 7x + 8 = 0

This equation can now be solved using the quadratic formula, which is given by:

x = ∛(-b ± √(b² - 4ac)) / (2a)

Where a, b, and c are the coefficients of the equation ax² + bx + c = 0. For our equation:

• a = 1
• b = -7
• c = 8

Plugging these values into the quadratic formula will give us the potential solutions for x. After calculation, if any solutions do match one of the options given (A, B, C, or D), that would be our answer to the nearest tenth. If using a graphing technology, the solutions are approximated and verified visually.