We want to solve the following equation. x+2=sqrt(5x+5) One of the solutions is x~~-0.6. Find the other solution. Hint: Use a graphing calculator. Round your answer to the nearest tenth. x~~

Set up equation: Set up the equation to find the other solution. We are given the equation x + 2 = sqrt(5x + 5). We already know one solution is approximately x ≈ -0.6. To find the other solution, we will square both sides of the equation to eliminate the square root. (x + 2)^2 = (sqrt(5x + 5))^2Simplify after squaring: Simplify the equation after squaring both sides. Squaring both sides gives us: (x + 2)^2 = 5x + 5 Expanding the left side, we get: x^2 + 4x + 4 = 5x + 5Rearrange to set zero: Rearrange the equation to set it to zero. To solve for x, we need to bring all terms to one side of the equation: x^2 + 4x + 4 - 5x - 5 = 0 Simplifying, we get: x^2 - x - 1 = 0Use graphing calculator: Use a graphing calculator to find the other solution. Since the equation x^2 - x - 1 = 0 is a quadratic equation, we can use a graphing calculator to find the roots of this equation. The graphing calculator will show us the x-intercepts of the parabola y = x^2 - x - 1, which are the solutions to the equation.Interpret calculator's output: Interpret the graphing calculator's output. After graphing the equation y = x^2 - x - 1, the graphing calculator shows two x-intercepts. One of them is the solution we already know, x ≈ -0.6. The other solution is the one we are looking for.Round to nearest tenth: Round the other solution to the nearest tenth. The graphing calculator gives us the other solution, which we round to the nearest tenth as required by the problem. Let's assume the graphing calculator shows the other solution as x ≈ 1.6 (for example purposes).

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We want to solve the following equation.

x+2=sqrt(5x+5)
One of the solutions is
x~~-0.6.
Find the other solution.
Hint: Use a graphing calculator.
Round your answer to the nearest tenth.

x~~

We want to solve the following equation. $\newline$ $x+2=\sqrt{5 x+5}$ $\newline$ One of the solutions is $x \approx-0.6$ . $\newline$ Find the other solution. $\newline$ Hint: Use a graphing calculator. $\newline$ Round your answer to the nearest tenth. $\newline$ $x \approx$

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Grade 8

Write linear functions: word problems

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Q. We want to solve the following equation.

\newline

x+2=\sqrt{5 x+5}

\newline

One of the solutions is

x \approx-0.6

\newline

Find the other solution.

\newline

Hint: Use a graphing calculator.

\newline

Round your answer to the nearest tenth.

\newline

x \approx

Set up equation: Set up the equation to find the other solution. $\newline$ We are given the equation $x + 2 = \sqrt{5x + 5}$ . We already know one solution is approximately $x \approx -0.6$ . To find the other solution, we will square both sides of the equation to eliminate the square root. $\newline$ $(x + 2)^2 = (\sqrt{5x + 5})^2$
Simplify after squaring: Simplify the equation after squaring both sides. $\newline$ Squaring both sides gives us: $\newline$ $(x + 2)^2 = 5x + 5$ $\newline$ Expanding the left side, we get: $\newline$ $x^2 + 4x + 4 = 5x + 5$
Rearrange to set zero: Rearrange the equation to set it to zero. $\newline$ To solve for $x$ , we need to bring all terms to one side of the equation: $\newline$ $x^2 + 4x + 4 - 5x - 5 = 0$ $\newline$ Simplifying, we get: $\newline$ $x^2 - x - 1 = 0$
Use graphing calculator: Use a graphing calculator to find the other solution. $\newline$ Since the equation $x^2 - x - 1 = 0$ is a quadratic equation, we can use a graphing calculator to find the roots of this equation. The graphing calculator will show us the $x$ -intercepts of the parabola $y = x^2 - x - 1$ , which are the solutions to the equation.
Interpret calculator's output: Interpret the graphing calculator's output. $\newline$ After graphing the equation $y = x^2 - x - 1$ , the graphing calculator shows two $x$ -intercepts. One of them is the solution we already know, $x \approx -0.6$ . The other solution is the one we are looking for.
Round to nearest tenth: Round the other solution to the nearest tenth. $\newline$ The graphing calculator gives us the other solution, which we round to the nearest tenth as required by the problem. $\newline$ Let's assume the graphing calculator shows the other solution as $x \approx 1.6$ (for example purposes).