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Chapter 11: Problem 2

$$x^{2}+8 x=-7$$ Quantity \(\mathbf{A}\) \(x\) Quantity_B 0 a. Quantity A is greater. b. Quantity B is greater. c. The two quantities are equal. d. The relationship cannot be determined from the information given.

Short Answer

Expert verified
b. Quantity B is greater.

Step by step solution

01

Rearrange the equation to standard form

The standard form of a quadratic equation is \( ax^{2} + bx + c = 0 \). We need to rearrange our equation: \( x^{2} + 8x + 7 = 0 \)
02

Apply the quadratic formula

The quadratic formula is \( x = [-b \pm sqrt(b^{2} - 4ac)] / 2a\). The values for \( a \), \( b \), and \( c \) from our equation are 1, 8, and 7 respectively. Plugging these into the formula, we get two possible solutions: \( x_{1} = (-8 + sqrt[(8^{2} - 4*1*7)]) / 2*1 = -1 \) , \( x_{2} = (-8 - sqrt[(8^{2} - 4*1*7)]) / 2*1 = -7 \)
03

Compare the quantities

Now compare the values of \( x \) to Quantity B, which is 0. Both \( x_1 = -1 \) and \( x_2 = -7 \) are smaller than 0 so Quantity B is greater.

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