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Solve for xx: x2+3x−10=0x^{2} + 3x - 10 = 0 a=1a=1, b=3b=3, and c=−10c=-10.

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Full solution

Q. Solve for xx: x2+3x−10=0x^{2} + 3x - 10 = 0 a=1a=1, b=3b=3, and c=−10c=-10.
  1. Identify type of equation: Identify the type of equation.\newlineThe equation x2+3x−10=0x^2 + 3x - 10 = 0 is a quadratic equation in the standard form ax2+bx+c=0ax^2 + bx + c = 0, where a=1a = 1, b=3b = 3, and c=−10c = -10.
  2. Apply quadratic formula: Apply the quadratic formula to solve for xx. The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. We will use this formula to find the values of xx.
  3. Calculate discriminant: Calculate the discriminant.\newlineThe discriminant is the part of the quadratic formula under the square root, b2−4acb^2 - 4ac. Let's calculate it:\newlineDiscriminant = (3)2−4(1)(−10)=9+40=49(3)^2 - 4(1)(-10) = 9 + 40 = 49.
  4. Calculate possible values for x: Calculate the two possible values for x.\newlineSince the discriminant is positive, there will be two real solutions for x.\newlinex=−3±492×1x = \frac{-3 \pm \sqrt{49}}{2 \times 1}\newlinex=−3±72x = \frac{-3 \pm 7}{2}
  5. Solve for values of xx: Solve for the two values of xx.\newlineFirst solution:\newlinex=(−3+7)/2x = (-3 + 7) / 2\newlinex=4/2x = 4 / 2\newlinex=2x = 2\newlineSecond solution:\newlinex=(−3−7)/2x = (-3 - 7) / 2\newlinex=−10/2x = -10 / 2\newlinex=−5x = -5

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