49x^(2)-64=0 What are the solutions to the given equation? Choose 1 answer: (A) x=(64)/(49) (B) x=-(64)/(49) and x=(64)/(49) (C) x=(8)/(7) (D) x=-(8)/(7) and x=(8)/(7)

Identify equation type and method: Identify the type of equation and the method to solve it. The given equation is a quadratic equation in the standard form ax^2 + bx + c = 0, where a = 49, b = 0, and c = -64. To solve for x, we can factor the equation or use the quadratic formula. Since the equation is already in a form that suggests factoring, we will attempt to factor it.Factor the quadratic equation: Factor the quadratic equation. The equation 49x^2 - 64 can be factored as a difference of squares because both 49x^2 and 64 are perfect squares. (7x)^2 - 8^2 = 0 (7x + 8)(7x - 8) = 0Solve for x: Set each factor equal to zero and solve for x. 7x + 8 = 0 or 7x - 8 = 0 For the first factor: 7x + 8 = 0 7x = -8 x = -8/7 For the second factor: 7x - 8 = 0 7x = 8 x = 8/7Check solutions in original equation: Check the solutions in the original equation. Substitute x = -8/7 into the original equation: 49(-8/7)^2 - 64 = 49(64/49) - 64 = 64 - 64 = 0 Substitute x = 8/7 into the original equation: 49(8/7)^2 - 64 = 49(64/49) - 64 = 64 - 64 = 0 Both solutions satisfy the original equation.

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49x^(2)-64=0
What are the solutions to the given equation?
Choose 1 answer:
(A)
x=(64)/(49)
(B)
x=-(64)/(49) and
x=(64)/(49)
(C)
x=(8)/(7)
(D)
x=-(8)/(7) and
x=(8)/(7)

$49 x^{2}-64=0$ $\newline$ What are the solutions to the given equation? $\newline$ Choose $1$ answer: $\newline$ (A) $x=\frac{64}{49}$ $\newline$ B $x=-\frac{64}{49}$ and $x=\frac{64}{49}$ $\newline$ (C) $x=\frac{8}{7}$ $\newline$ (D) $x=-\frac{8}{7}$ and $x=\frac{8}{7}$

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Full solution

49 x^{2}-64=0

\newline

What are the solutions to the given equation?

\newline

Choose

1

answer:

\newline

(A)

x=\frac{64}{49}

\newline

x=-\frac{64}{49}

and

x=\frac{64}{49}

\newline

(C)

x=\frac{8}{7}

\newline

(D)

x=-\frac{8}{7}

and

x=\frac{8}{7}

Identify equation type and method: Identify the type of equation and the method to solve it. $\newline$ The given equation is a quadratic equation in the standard form $ax^2 + bx + c = 0$ , where $a = 49$ , $b = 0$ , and $c = -64$ . $\newline$ To solve for $x$ , we can factor the equation or use the quadratic formula. Since the equation is already in a form that suggests factoring, we will attempt to factor it.
Factor the quadratic equation: Factor the quadratic equation. $\newline$ The equation $49x^2 - 64$ can be factored as a difference of squares because both $49x^2$ and $64$ are perfect squares. $\newline$ $(7x)^2 - 8^2 = 0$ $\newline$ $(7x + 8)(7x - 8) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ $7x + 8 = 0$ or $7x - 8 = 0$ $\newline$ For the first factor: $\newline$ $7x + 8 = 0$ $\newline$ $7x = -8$ $\newline$ $x = -\frac{8}{7}$ $\newline$ For the second factor: $\newline$ $7x - 8 = 0$ $\newline$ $7x = 8$ $\newline$ $x = \frac{8}{7}$
Check solutions in original equation: Check the solutions in the original equation. $\newline$ Substitute $x = -\frac{8}{7}$ into the original equation: $\newline$ $49\left(-\frac{8}{7}\right)^2 - 64 = 49\left(\frac{64}{49}\right) - 64 = 64 - 64 = 0$ $\newline$ Substitute $x = \frac{8}{7}$ into the original equation: $\newline$ $49\left(\frac{8}{7}\right)^2 - 64 = 49\left(\frac{64}{49}\right) - 64 = 64 - 64 = 0$ $\newline$ Both solutions satisfy the original equation.