Rewrite in Standard Form: Start by rewriting the equation in standard form, which means getting all terms on one side of the equation and setting it equal to zero. 5x^2 = 30x - 45 Subtract 30x and add 45 to both sides to get: 5x^2 - 30x + 45 = 0Factor the Quadratic: Check if the quadratic equation can be factored. Look for two numbers that multiply to 5*45 (225) and add up to -30. The numbers that satisfy these conditions are -15 and -15, since (-15)*(-15) = 225 and (-15) + (-15) = -30. So, we can factor the quadratic as: 5x^2 - 30x + 45 = (5x - 15)(x - 3) = 0Solve for x: Set each factor equal to zero and solve for x. First factor: 5x - 15 = 0 Add 15 to both sides: 5x = 15 Divide by 5: x = 3 Second factor: x - 3 = 0 Add 3 to both sides: x = 3Check for Errors: Check for any potential math errors in the previous steps. We factored the quadratic correctly and solved for x without making any arithmetic mistakes.

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$5 x^{2}=30 x-45$

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Algebra 2

Solve complex trigonomentric equations

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5 x^{2}=30 x-45

Rewrite in Standard Form: Start by rewriting the equation in standard form, which means getting all terms on one side of the equation and setting it equal to zero. $\newline$ $5x^2 = 30x - 45$ $\newline$ Subtract $30x$ and add $45$ to both sides to get: $\newline$ $5x^2 - 30x + 45 = 0$
Factor the Quadratic: Check if the quadratic equation can be factored. Look for two numbers that multiply to $5\times45$ $(225)$ and add up to $-30$ . The numbers that satisfy these conditions are $-15$ and $-15$ , since $(-15)\times(-15) = 225$ and $(-15) + (-15) = -30$ . So, we can factor the quadratic as: $5x^2 - 30x + 45 = (5x - 15)(x - 3) = 0$
Solve for x: Set each factor equal to zero and solve for x. $\newline$ First factor: $5x - 15 = 0$ $\newline$ Add $15$ to both sides: $5x = 15$ $\newline$ Divide by $5$ : $x = 3$ $\newline$ Second factor: $x - 3 = 0$ $\newline$ Add $3$ to both sides: $x = 3$
Check for Errors: Check for any potential math errors in the previous steps. We factored the quadratic correctly and solved for $x$ without making any arithmetic mistakes.