Answer:
[tex]x = - \frac{7}{4} \: \frac{1}{2} [/tex]
Step-by-step explanation:
[tex]8 {x}^{2} + 14x - 4x - 7 = 0 \\ 2x(4x + 7) - (4x + 7) = 0 \\ (4x + 7)(2x - 1) = 0[/tex]
Answer:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
Step-by-step explanation:
Given: 8x² + 10x - 7 = 0
When factoring trinomials of the form ax² + bx + c:
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:
Case 1:
⇒ 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 = [tex]\bold{-\dfrac{7}{4}}[/tex]
Case 2:
⇒ 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 = [tex]\bold{\dfrac{1}{2}}[/tex]
Solutions:
[tex]\large \text{$x_1$}=-\dfrac{7}{4}, \large \text{$x_2$}=\dfrac{1}{2}[/tex]
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