Check if the expression is quadratic equation (x-5)^2+1=3x-4
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We have the expression: (x-5)^2 + 1 = 3x - 4
(x-5)^2 + 1 = 3x - 4
open the brackets
x^2 + 25 - 10x + 1 = 3x - 4
=> x^2 - 10x - 3x + 26 + 4 = 0
=> x^2 - 13x + 30 = 0
The expression is a quadratic equation.
If we have to find the solutions
x^2 - 13x + 30 = 0
=> x^2 - 10x - 3x + 30 = 0
=> x(x - 10) - 3( x - 10) = 0
=> (x - 3)(x - 10) = 0
=> x = 3 and x = 10
The given expression is a quadratic equation.
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For the given expression to represent a quadratic equation, it has to have the following form: ax^2 + bx + c = 0.
We'll begin by expanding the square from the left side:
(x-5)^2 = x^2 - 10x + 25
We'll re-write the equation:
x^2 - 10x + 25 + 1 = 3x - 4
We'll combine like terms from the left side:
x^2 - 10x + 26 = 3x - 4
We'll subtract 3x - 4:
x^2 - 10x + 26 - 3x + 4 = 0
We'll combine like terms:
x^2 - 13x + 30 = 0
The final result is a quadratic equation x^2 - 13x + 30 = 0.
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