Solve the equation by factoring 2x^2+7x=4

x = - 4 , x =

Step-by-step explanation:

given 2x² + 7x = 4

rearrange into standard form : ax² + bx + c = 0 : a ≠ 0

subtract 4 from both sides

2x² + 7x - 4 = 0 ← in standard form

Consider the product of the factors of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term, that is

product = 2 × - 4 = - 8 and sum = + 7

The factors are + 8 and - 1

use these factors to split the middle term

2x² + 8x - x - 4 = 0 ( factor by grouping first/second and third/fourth terms )

2x(x + 4) - 1(x + 4) = 0 ( take out the common factor (x + 4) )

(x + 4)(2x - 1) = 0

equate each factor to zero and solve for x

x + 4 = 0 ⇒ x = - 4

2x - 1 = 0 ⇒ 2x = 1 ⇒ x =

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step-by-step explanation: