Solve the system of equations. y = 21x + 44 y = x^2 + 3x + 25 Write the coordinates in exact form. Simplify all fractions and radicals. (______,______) (______,______)

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Solve the system of equations. y = 21x + 44 y = x^2 + 3x + 25    Write the coordinates in exact form. Simplify all fractions and radicals.  (______,______) (______,______)

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Set Equations Equal: Set the two equations equal to each other since they both equal y. This gives us 21x + 44 = x^2 + 3x + 25.Rearrange and Simplify: Rearrange the equation to set it to zero by subtracting 21x + 44 from both sides. This gives us x^2 + 3x + 25 - 21x - 44 = 0, which simplifies to x^2 - 18x - 19 = 0.Factor Quadratic Equation: Factor the quadratic equation x^2 - 18x - 19 = 0. This equation does not factor nicely, so we will use the quadratic formula x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -18, and c = -19.Calculate Discriminant: Calculate the discriminant Δ = b^2 - 4ac which is Δ = (-18)^2 - 4(1)(-19). This gives us Δ = 324 + 76, which simplifies to Δ = 400.Use Quadratic Formula: Since the discriminant is positive, we have two real solutions. Calculate the solutions using the quadratic formula: x = (18 ± √400) / 2. This simplifies to x = (18 ± 20) / 2.Find Values of x: Find the two values of x. The first value is x = (18 + 20) / 2 which simplifies to x = 38 / 2, giving us x = 19. The second value is x = (18 - 20) / 2 which simplifies to x = -2 / 2, giving us x = -1.Substitute x = 19: Substitute x = 19 into the original equation y = 21x + 44 to find the corresponding y-value. This gives us y = 21(19) + 44, which simplifies to y = 399 + 44, giving us y = 443.Substitute x = -1: Substitute x = -1 into the original equation y = 21x + 44 to find the corresponding y-value. This gives us y = 21(-1) + 44, which simplifies to y = -21 + 44, giving us y = 23.

Solve the system of equations. $\newline$ $y = 21x + 44$ $\newline$ $y = x^2 + 3x + 25$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)

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Solve the system of equations.\newliney=21x+44y = 21x + 44y=21x+44\newliney=x2+3x+25y = x^2 + 3x + 25y=x2+3x+25\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)

Solve the system of equations. $\newline$ $y = 21x + 44$ $\newline$ $y = x^2 + 3x + 25$ $\newline$ Write the coordinates in exact form. Simplify all fractions and radicals. $\newline$ (,) $\newline$ (,)