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Computer Science
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Step-by-step solution
5 stepsTo solve for x in the equation 2x² + 5x - 3 = 0, we can use the quadratic formula.
The quadratic formula is:
x = [-b ± √(b² - 4ac)] / (2a)
Identify the coefficients a, b, and c from the equation 2x² + 5x - 3 = 0.
Here, a = 2, b = 5, and c = -3.
Substitute these values into the quadratic formula.
x = [-5 ± √(5² - 4 × 2 × -3)] / (2 × 2)
Simplify the expression under the square root (the discriminant).
x = [-5 ± √(25 - (-24))] / 4
x = [-5 ± √(25 + 24)] / 4
x = [-5 ± √49] / 4Calculate the square root.
x = [-5 ± 7] / 4
Find the two possible values for x by using the plus and minus signs separately.
For the plus sign:
x₁ = (-5 + 7) / 4
x₁ = 2 / 4
x₁ = (1)/(2)For the minus sign:
x₂ = (-5 - 7) / 4
x₂ = -12 / 4
x₂ = -3The solutions for x are (1)/(2) and -3.
The solutions are x = (1)/(2) and x = -3.
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