Question

Solve each equation. $5 m^{2}+8=22 m$

   Solve each equation.
$5 m^{2}+8=22 m$

Beginning and Intermediate Algebra

Beginning and Intermediate Algebra

Sherri Messersmith 3rd Edition

Chapter 11, Problem 9

Instant Answer

Solved by Expert Ashley Volpe

06/25/2020

Step 1

To do this, subtract 22m from both sides of the equation: $5m^2 - 22m + 8 = 0$ Show more…

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Solve each equation. $5 m^{2}+8=22 m$

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Key Concepts

Quadratic Equations

A quadratic equation is a second-degree polynomial equation typically presented in the form ax² + bx + c = 0, where a, b, and c are constants and a is non-zero. This type of equation arises in various mathematical and applied contexts and usually involves determining the values of the variable that satisfy the equation.

Standard Form

Rewriting the equation in standard form (ax² + bx + c = 0) is essential for systematic analysis and solution of quadratic equations. This form allows for the straightforward application of solving techniques such as factoring, completing the square, or using the quadratic formula.

Quadratic Formula

The quadratic formula, given by m = (-b ± ?(b² - 4ac)) / (2a), is a universal method for solving any quadratic equation once it is in standard form. It provides a direct way to find the roots by substituting the coefficients a, b, and c, particularly when the quadratic does not factor easily.

Discriminant

The discriminant, calculated as b² - 4ac, is a component of the quadratic formula that indicates the nature of the roots. It helps determine whether the equation has two distinct real roots, one real repeated root, or two complex roots, thus offering insight into the behavior of the quadratic function.

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