Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)² - (2x + 3) - 14 = 0.
Quadratic Equations
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Question

Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)² - (2x + 3) - 14 = 0.

KnowledgeBoat · Accepted Answer

Substituting, 2x + 3 = y in 4(2x + 3)² - (2x + 3) - 14 = 0 we get, ⇒ 4y² - y - 14 = 0 ⇒ 4y² - 8y + 7y - 14 = 0 ⇒ 4y(y - 2) + 7(y - 2) = 0 ⇒ (4y + 7)(y - 2) = 0 ⇒ 4y + 7 = 0 or y - 2 = 0 ⇒ 4y = -7 or y = 2 ⇒ y = or y = 2. ∴ 2x + 3 = or 2x + 3 = 2 ⇒ 2x = or 2x = 2 - 3 ⇒ 2x = or 2x = -1 ⇒ 2x = ⇒ x = Hence, x = .

Mathematics

Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)² - (2x + 3) - 14 = 0.

Quadratic Equations

Related Questions

Find the value of x, if a + 7 = 0; b + 10 = 0 and 12x² = ax - b.

Mathematics

Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)2 - (2x + 3) - 14 = 0.

Quadratic Equations

Related Questions

Find the value of x, if a + 7 = 0; b + 10 = 0 and 12x2 = ax - b.

Use the substitution 2x + 3 = y to solve for x, if 4(2x + 3)² - (2x + 3) - 14 = 0.

Find the value of x, if a + 7 = 0; b + 10 = 0 and 12x² = ax - b.