Chapter 10: Q. 141 (page 1196)

Solve the equation $x^{2} + 10 x = 200$
a) by completing the square
b) using the Quadratic Formula
c) Which method do you prefer? Why?

Short Answer

Expert verified

$x = - 20, 10 .$

Step by step solution

Step 1. Given

$Given equation is, x^{2} + 10 x = 200 .$

Step 1. Part ( a )

$Using completing the square method, x^{2} + 10 x - 200 = 0 x^{2} + 2 (5) (x) + {(5)}^{2} - {(5)}^{2} - 200 = 0 {(x + 5)}^{2} - {(15)}^{2} = 0 Using identity, a^{2} - b^{2} = (a - b) (a + b) (x + 5 - 15) (x + 5 + 15) = 0 x = - 20, x = 10 .$

Step 3. Part ( b )

$U \sin g q u a d r a t i c f o r m u l a, x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}, x^{2} + 10 x - 200 = 0 N o w, x = \frac{- 10 \pm \sqrt{{(10)}^{2} - 4 (1) (- 200)}}{2} x = \frac{- 10 \pm \sqrt{900}}{2} x = \frac{- 10 + 30}{2} = 10, x = \frac{- 10 - 30}{2} = - 20$

Step 4. Part ( c )

Quadratic formula – is the method that is used most often for solving a quadratic equation. If you are using factoring or the quadratic formula, make sure that the equation is in standard form.

Step 5. Check part

Verifying that the roots of given equation is -20 and 10 .

${(- 20)}^{2} + 10 (- 20) = 400 - 200 = 200 = R . H . S {(10)}^{2} + 10 (10) = 100 + 100 = 200 = R . H . S$

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Solve the equation $x^{2} + 10 x = 200$
a) by completing the square
b) using the Quadratic Formula
c) Which method do you prefer? Why?

Short Answer

Step by step solution

Step 1. Given

Step 1. Part ( a )

Step 3. Part ( b )

Step 4. Part ( c )

Step 5. Check part

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Solve the equation x2+10x=200a) by completing the squareb) using the Quadratic Formulac) Which method do you prefer? Why?

Short Answer

Step by step solution

Step 1. Given

Step 1. Part ( a )

Step 3. Part ( b )

Step 4. Part ( c )

Step 5. Check part

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Discrete Mathematics

Decision Maths

Calculus

Statistics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

Solve the equation $x^{2} + 10 x = 200$
a) by completing the square
b) using the Quadratic Formula
c) Which method do you prefer? Why?