Answer:
Step-by-step explanation:
[tex]4x^2+3x=24-x\qquad\text{subtract 24 from both sides}\\\\4x^2+3x-24=-x\qquad\text{add}\ x\ \text{to both sides}\\\\4x^2+4x-24=0\qquad\text{divide both sides by 4}\\\\x^2+x-6=0\\\\x^2+3x-2x-6=0\\\\x(x+3)-2(x+3)=0\\\\(x+3)(x-2)=0\iff x+3=0\ \vee\ x-2=0\\\\x+3=0\qquad\text{subtract 3 from both sides}\\x=-3\\\\x-2=0\qquad\text{add 2 to both sides}\\x=2[/tex]
The given equation, 4·x² + 3·x = 24 - x, can be simplified and factorized
to give the solution as; -3, 2
The solution to the given equation, 4·x² + 3·x = 24 - x, is the point of
intersection of the parabola, 4·x² + 3·x, and the line, 24 - x
The solution is therefore, found as follows;
4·x² + 3·x = 24 - x
4·x² + 3·x - (24 - x) = 0
4·x² + 4·x - 24 = 0
Dividing by 4, gives;
4·(x² + x - 6) = 0
x² + x - 6 = 0 ÷ 4 = 0
Factorizing, the above quadratic equation, we have;
(x + 3) × (x - 2) = 0
The solution of the equation is therefore;
Learn more about factorizing quadratic equations here:
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