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Ch. 1 - Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook
All textbooksBlitzer 8th EditionCh. 1 - Equations and InequalitiesProblem 85
Chapter 2, Problem 85

Solve each equation in Exercises 83–108 by the method of your choice. 5x2+2=11x5x^2 + 2 = 11x

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Rewrite the given equation to standard quadratic form by moving all terms to one side: \(5x^2 + 2 = 11x\) becomes \(5x^2 - 11x + 2 = 0\).
Identify the coefficients in the quadratic equation \(ax^2 + bx + c = 0\): here, \(a = 5\), \(b = -11\), and \(c = 2\).
Use the quadratic formula to solve for \(x\): \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).
Calculate the discriminant \(\Delta = b^2 - 4ac\) to determine the nature of the roots.
Substitute the values of \(a\), \(b\), and \(c\) into the quadratic formula and simplify under the square root and the entire expression to find the solutions for \(x\).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Quadratic Equations

A quadratic equation is a polynomial equation of degree two, generally written as ax² + bx + c = 0. Solving such equations involves finding the values of x that satisfy the equation. Recognizing the standard form is essential for applying appropriate solution methods.
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Rearranging Equations

Rearranging involves moving all terms to one side to set the equation equal to zero. This step is crucial for quadratic equations because it allows the equation to be expressed in standard form, enabling the use of factoring, completing the square, or the quadratic formula.
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Methods for Solving Quadratic Equations

Common methods include factoring, completing the square, and using the quadratic formula. Factoring works when the quadratic can be expressed as a product of binomials. The quadratic formula applies universally and is derived from completing the square.
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Related Practice
Textbook Question

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2/x + 1/2 = 3/4

Textbook Question

Solve each equation in Exercises 83–108 by the method of your choice. 2x2 - x = 1

Textbook Question

Solve each absolute value inequality. - 4|1 - x| < - 16

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Textbook Question

Solve each polynomial equation in Exercises 86–87. 2x^4 = 50 x^2

Textbook Question

In Exercises 59–94, solve each absolute value inequality. 3 ≤ |2x - 1|

Textbook Question

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. ∣2x2−4∣=∣2x2∣|2x^2 - 4| = |2x^2|

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