Solve the equation x, squared, plus, 13, x, plus, 27, equals, 0x 2 +13x+27=0 to the nearest tenth.
Question
Solve the equation x, squared, plus, 13, x, plus, 27, equals, 0x 2 +13x+27=0 to the nearest tenth.
Solution
To solve the quadratic equation x^2 + 13x + 27 = 0, we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 1, b = 13, and c = 27.
Step 1: Calculate the value under the square root, b^2 - 4ac = (13)^2 - 4127 = 169 - 108 = 61.
Step 2: Calculate the values of x using the quadratic formula:
x = [-13 ± sqrt(61)] / (2*1)
So, the solutions are:
x1 = [-13 + sqrt(61)] / 2 = -3.2 (rounded to the nearest tenth)
x2 = [-13 - sqrt(61)] / 2 = -8.8 (rounded to the nearest tenth)
So, the solutions to the equation x^2 + 13x + 27 = 0 are x = -3.2 and x = -8.8.
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