What substitution should be used to rewrite 6(x + 5)² + 5(x + 5) - 4 = 0 as a quadratic equation?

Solution:

Quadratic equations are second-degree algebraic expressions and are of the form ax² + bx + c = 0.

Given: 6(x + 5)² + 5(x + 5) – 4 = 0

Let x + 5 = t

Thus, the given equation can now be written as,

6t² + 5t - 4 = 0

6t² + 8t - 3t - 4 = 0 [Splitting the middle term 5t]

2t (3t + 4) - 1(3t + 4) = 0

(3t + 4) (2t - 1) = 0

3t + 4 = 0, 2t - 1 = 0

Thus, t = -4/3, t = 1/2

We know that t = x + 5

Thus, 

x + 5 = -4/3 and x + 5 = 1/2

x = -19/3 and x = -9/2

We can also use Cuemath's Online Quadratic equation calculator to find the roots of an equation.

Thus, the substitution used to rewrite 6(x + 5)² + 5(x + 5) – 4 = 0 as a quadratic equation is x + 5 = t and the values of x are -19/3 and -9/2.

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What substitution should be used to rewrite 6(x + 5)² + 5(x + 5) - 4 = 0 as a quadratic equation?

Summary:

The substitution used to rewrite 6(x + 5)² + 5(x + 5) - 4 = 0 as a quadratic equation is x + 5 = t and the values of x are -19/3 and -9/2.