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Solve for x. 2x^(2)+6=-7x

Solve for x x .\newline2x2+6=−7x 2 x^{2}+6=-7 x

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Full solution

Q. Solve for x x .\newline2x2+6=−7x 2 x^{2}+6=-7 x
  1. Factor the quadratic equation: Now, we need to factor the quadratic equation.\newlineLooking for two numbers that multiply to 2×6=122\times 6=12 and add up to 77.\newlineThe numbers are 33 and 44.\newlineSo, we can write the equation as (2x+3)(x+2)=0(2x + 3)(x + 2) = 0
  2. Find two numbers: Next, we set each factor equal to zero and solve for xx.\newlineFirst factor: 2x+3=02x + 3 = 0\newlineSubtract 33 from both sides: 2x=−32x = -3\newlineDivide by 22: x=−32x = -\frac{3}{2}
  3. Set factors equal to zero: Now, solve the second factor: x+2=0x + 2 = 0 Subtract 22 from both sides: x=−2x = -2

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