Question

Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$. $$ 36 c^{2}-36 c+25=0 $$

Name: Problem 71, Chapter 8: Intermediate Algebra for College Students
Uploaded: 2020-07-13T17:39:47-08:00
Duration: 36 s
Channel: Ankit Gupta
Description: Solve each equation by completing the square. Write complex number solutions in the form a ±b i. 36 c^2-36 c+25=0

   Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$.
$$
36 c^{2}-36 c+25=0
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 8, Problem 71

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

$$ c^2 - c + \frac{25}{36} = 0 $$ Show more…

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Solve each equation by completing the square. Write complex number solutions in the form $a \pm b i$. $$ 36 c^{2}-36 c+25=0 $$

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Key Concepts

Complex Numbers

When solving quadratic equations, if the process under the square root (the discriminant) is negative, the solution involves complex numbers. Complex numbers combine a real part and an imaginary part (using the imaginary unit i defined as the square root of -1), and are typically expressed in the form a ± bi.

Completing the Square

Completing the square is a method used to transform a quadratic expression into a perfect square plus a constant. This technique involves re-arranging and adjusting the equation so that one side becomes a squared binomial, making it simpler to solve the equation, especially when extracting square roots.

Quadratic Equations

Quadratic equations are second-degree polynomial equations that generally take the form ax² + bx + c = 0. They can have two real solutions or two complex solutions depending on the value of the discriminant, and are foundational in algebra and calculus.

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