If (40+x)^2=2209,then x is
Answers
Answer:
12 x 2−17 x −40=0. Enter an ... Step-1 : Multiply the coefficient of the first term by the constant 12 • -40 = -480. Step-2 ... then, according to the law of transitivity, (x-(17/24))2 = 2209/576
Concept
An algebraic equation of the second degree in x is a quadratic equation. The quadratic equation is written as ax² + bx + c = 0, where x is the variable, a and b are the coefficients, and c is the constant term. First, there must be a term other than zero in the coefficient of x² (a ≠ 0) for an equation to be a quadratic equation. The x² term is written first when constructing a quadratic equation in standard form, then the x term, and finally the constant term.
Given
(40₊x)² = 2209
Find
The given equation must be solved in order to determine the value of x.
Solution
given, (40₊x)² = 2209
expand the equation which is in the form of (a₊b)² = a²₊b²₊2ab
(40)² ₊ (x)² ₊ 2(40)(x) = 2209
1600 ₊ x² ₊ 80x = 2209
x² ₊ 80x ₊ 1600 = 2209
x² ₊ 80x ₊ 1600 ₋ 2209 = 0
x² ₊ 80x ₋ 609 = 0
factorizing the above equation.
x² ₋ 7x ₊ 87x ₋ 609 = 0
x(x₋7) ₊ 87(x₋7) = 0
(x ₋ 7)(x ₊ 87) = 0
x = 7 or x = ₋87
hence after solving the equation we get the value for x as 7 or ₋87
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