How do I solve this equation by completing the square. 4X^2 + 12x +5 = 21
1 answer:
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I think your question is missed of key information, allow me to add in and hope it will fit the original one. Please have a look at the attached photo.
My answer:
Scale Drawing Lengths: . . / .
Actual Court Lengths . . .
Scale Factor: inch corresponds to ( ∙ ) inches, or inches, so the scale factor is .
Let = , represent the scale drawing lengths in inches, and represent the actual court lengths in inches. The -values must be converted from feet to inches.
To find actual length:
= =
() = inches, or feet
To find actual width:
= = ( )
= / ∙ /
= inches, or feet
The actual court measures feet by feet. Yes, the lot is big enough for the court Vincent planned. The court will take up the entire width of the lot.
Answer:
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
<u>When factoring trinomials of the form ax² + bx + c</u>:
- multiply the leading coefficient and the last term.
- find the product factors that add to give you the coefficient of the middle term.
- rewrite the polynomial with those factors replacing the middle term.
1. Split the middle term:
⇒ 8 × -7 = -56 [multiply the leading coefficient and the last term]
⇒ 14, -4 [find the product factors that add to the middle term's coefficient]
⇒ 8x² + 14x - 4x - 7 = 0 [rewrite with those factors replacing the middle term.]
2. Factor by grouping:
⇒ 8x² + 14x - 4x - 7 = 0 [factor out 2x]
⇒ 2x(4x + 7) - 4x - 7 = 0 [factor out -1 or the negative sign]
⇒ 2x(4x + 7) -1(4x + 7) = 0 [factor out 4x + 7]
⟹ (4x + 7)(2x - 1) = 0
3. Separate into 2 cases:
- 4x + 7 = 0
- 2x - 1 = 0
<u><em>Case 1:</em></u>
⇒ 4x + 7 = 0 [subtract 7 from both sides]
⇒ 4x + 7 - 7 = 0 - 7
⇒ 4x = -7 [divide both sides by 4]
⇒ 4x ÷ 4 = -7 ÷ 4
⟹ x =
<u><em>Case 2:</em></u>
⇒ 2x - 1 = 0 [subtract 1 from both sides]
⇒ 2x - 1 + 1 = 0 + 1
⇒ 2x = 1 [divide both sides by 2]
⇒ 2x ÷ 2 = 1 ÷ 2
⟹ x =
Solutions:
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