9-5 Co m p l e t i n g t h e Sq u a r e
Quick Review Ex e r c i se s
You can solve any quadratic equation by writing it in the Solve each equation by completing the square. If
form x2 + bx = c, completing the square, and finding the
square roots of each side of the equation.necessary, round to the nearest hundredth.- x 2 + 6x-5 = 0 31. x2 = 3x — 1
Ex a m p l e 32. 2x2 + 7x = —^6 33. x2 + lOx = -8What are the solutions of x2 + 8x = 513? 34. 4x2-8 x = 2 4 35. x2 - 14x + 16 = 0
x2 + 8x+16 = 513 + 16 Add (|)2, or 16, 36. Construction You are planning a rectangular patio
to each side. with length that is 7 ft less than three times its
(x + 4)2 = 529 Write x2 + 8x + 16 width. The area of the patio is 120 ft2. What are the
as a sq uare. dimensions of the patio?
x + 4 = ± V529 Find the square roots. 37. Design You are designing a rectangular birthday
x + 4 = +23 Simplify. card for a friend. You want the card's length to be
x + 4 = 23 or x + 4 = -2 3 Write as tw o equations.
x=19 or x=-27 Solve fo r x.1 in. more than twice the card’s width. The area of the
card is 88 in.2. What are the dimensions of the card?9-6 The Qu ad r at i c Fo r m u l a an d t he D i scr i m i n an t
Quick Review
You can solve the quadratic equation ax2 + bx + c = 0,
where a i= 0, by using the quadratic form ula
x = b ~ ^ 2 a - -4ac. The discriminant is b2 - 4ac.
The discriminant tells you how many real-number solutions
the equation has.
Ex a m p l e
How many real-number solutions does the equation
x2 + 3 = 2x have?
x2 - 2x + 3 = 0 Write in standard form.
b2 - 4ac = (—2)2 - 4(1)(3) Evaluate discriminant.
= —8 Simplify.Because the discriminant is negative, the equation has no
real-number solutions.
V V
Ex e r c i s e s
Find the number of real-number solutions of each
equation.- x2 + 7x - 10 = 3 39. 3x2 - 2 = 5x
Solve each equation using the quadratic formula. Round
to the nearest hundredth.- 4x2 + 3x - 8 = 0 41. 2x2 — 3x = 20
- x 2 + 8x + 4 = 5 43. 64x2 + 12x - 1 = 0
Solve each equation using any method. Explain why you
chose the method you used.- 5x2 - 10 = x2 + 90 45. x2 - 6x + 9 = 0
- Vertical Motion A ball is thrown into the air. The
height h, in feet, of the ball can be modeled by the
equation h = — 16r2 + 20f + 6, where t is the time, in
seconds, the ball is in the air. When will the ball hit
the ground?
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