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Chapter 6: Problem 76

Solve each equation by the method of your choice. \(x(x+1)=4-(x+2)(x+2)\)

Short Answer

Expert verified
The roots of the equation are \(x=\frac{-5\pm\sqrt{41}}{4}\)

Step by step solution

01

Expand the Brackets

Expand the equation: \(x^2+x=4-x^2-4x-4\).
02

Simplify the Equation

Simplify the equation by adding \(x^2\) and \(4x\) on both sides to get rid of the negative sign: \(2x^2+5x-4=0\).
03

Solve the Quadratic Equation

Utilize the quadratic formula \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\) where a = 2, b = 5 and c = -4 to find the roots: \(x=\frac{-5\pm\sqrt{5^2-4*2* -4}}{2*2}= \frac{-5\pm\sqrt{41}}{4}\).

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Most popular questions from this chapter

Explain how to factor \(x^{2}-5 x+6\).

In Exercises 33-36, solve each equation using the zero-product principle. \(x^{2}+8 x+15=0\)

Factor the trinomials , or state that the trinomial is prime. Check your factorization using FOIL multiplication. \(3 x^{2}-2 x-5\)

Use FOIL to find the products in Exercises 1-8. \((x+3)(x+5)\)

Solve each equation by the method of your choice. \(2 x^{2}-9 x-3=9-9 x\)
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