Chapter 9: Q16. (page 597)

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - 10 x = - 15$

Short Answer

Expert verified

The solutions of the quadratic equations are 8.2 and 1.8.

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 $x^{2} - 10 x = - 15$ . The equation can be rewritten as $x^{2} - 10 x + 15 = 0$ . Using quadratic formula $x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ , substitute 1 for $a, - 10$ for b and 15 for c.

Put the values in the formula and get $x = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 \times (1) \times (15)}}{2 (1)}$ .

Step 3. Write the solutions.

Simplify the expression for x.

$x = \frac{- (- 10) \pm \sqrt{{(- 10)}^{2} - 4 \times (1) \times (15)}}{2 (1)} = \frac{10 \pm \sqrt{100 - 60}}{2} = \frac{10 \pm 2 \sqrt{10}}{2} = 5 \pm \sqrt{10}$

Therefore, either

$x = 5 + \sqrt{10} = 8.2$

or,

$x = 5 - \sqrt{10} = 1.8$

that is., either $x = 8.2$ or $x = 1.8$ .

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Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - 10 x = - 15$

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.x2−10x=−15

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

Applied Mathematics

Discrete Mathematics

Theoretical and Mathematical Physics

Calculus

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

Solve the equation by using the Quadratic formula. Round to the nearest tenth if necessary.
$x^{2} - 10 x = - 15$