Solve the equation for all real solutions in simplest form.2, w, squared, minus, 5, w, minus, 9, equals, minus, 12w 2 −5w−9=−1

Question

$2w^2 - 5w - 9 = -12$

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To solve the equation 2w^2 - 5w - 9 = -12w^2 - 5w - 9 = -1, we can follow these steps:

Step 1: Combine like terms on both sides of the equation. -12w^2 - 5w - 9 + 12w^2 - 5w - 9 = -1 + 9 + 9

Simplifying, we get: -10w = -1 + 9 + 9

Step 2: Combine the constants on the right side of the equation. -10w = 17

Step 3: Divide both sides of the equation by -10 to solve for w. w = 17 / -10

Step 4: Simplify the fraction, if possible. w = -17/10

Therefore, the solution to the equation 2w^2 - 5w - 9 = -1 is w = -17/10.

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