Question

Michaela and Grace were trying to solve the equation: 4 x 2 − 100 = 0 4x 2 −100=04, x, squared, minus, 100, equals, 0 Michaela said, “I'll factor the left-hand side of the equation as ( 2 x + 10 ) ( 2 x − 10 ) (2x+10)(2x−10)left parenthesis, 2, x, plus, 10, right parenthesis, left parenthesis, 2, x, minus, 10, right parenthesis and solve using the zero product property.” Grace said, “I'll isolate the x 2 x 2 x, squared term by adding 100 100100 and dividing by 4 44 on both sides of the equation. Then I'll solve by taking the square root.” Whose solution strategy would work?

Answer 1

Both Michaela's factoring and Grace's square root isolation methods are correct for solving the equation 4x^2 - 100 = 0. They lead to the same solutions: x = -5 or x = 5.

Step-by-step explanation:

Both Michaela and Grace's solution strategies to solve the equation 4x^2 - 100 = 0 will work, as they are valid algebraic methods of solving quadratic equations. Michaela's approach involves factoring the quadratic equation and then using the zero product property to find the roots, where the equation factors into (2x + 10)(2x - 10) = 0. On the other hand, Grace's approach involves rearranging the equation by isolating the x^2 term, giving x^2 = 25, and then taking the square root of both sides to solve for x.

The zero product property states that if a product of two factors is zero, at least one of the factors must be zero. In the case of Michaela's factored form, we would set each factor equal to zero: 2x + 10 = 0 and 2x - 10 = 0, solving for x to get x = -5 and x = 5, respectively.

Grace's method would involve solving for x^2 = 25, where taking the square root of both sides yields x = ±5, since both 5 and -5 when squared give 25.

Answer 2

Both.

Step-by-step explanation:

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