Chapter 9: Q15. (page 597)

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - x - 30 = 0$

Short Answer

Expert verified

The solutions of the quadratic equations are 6 and $- 5$ .

Step by step solution

Step 1. Understand the concept used.

If $a x^{2} + b x + c = 0$ , with $a \neq 0$ , then $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ . Solving using factoring can be done by splitting the middle term of equation and then making groups and equating them to zero.

Step 2. Substitute the values.

It is given that $x^{2} - x - 30 = 0$ . Using quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 1 for $a, - 1$ for b and $- 30$ for c.

Put the values in the formula and get $x = \frac{- (- 1) \pm \sqrt{{(- 1)}^{2} - 4 \times (1) \times (- 30)}}{2 (1)}$ .

Step 3. Write the solutions.

Simplify the expression for x.

$x = \frac{- (- 1) \pm \sqrt{{(- 1)}^{2} - 4 \times (1) \times (- 30)}}{2 (1)} = \frac{1 \pm \sqrt{1 + 120}}{2} = \frac{1 \pm 11}{2}$

Therefore, either

$x = \frac{1 + 11}{2} = 6$

or,

$x = \frac{1 - 11}{2} = - 5$

that is., either $x = 6$ or $x = - 5$ .

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Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - x - 30 = 0$

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

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Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.x2−x−30=0

Short Answer

Step by step solution

Step 1. Understand the concept used.

Step 2. Substitute the values.

Step 3. Write the solutions.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Decision Maths

Logic and Functions

Applied Mathematics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - x - 30 = 0$