Solve the equation x, squared, plus, 14, x, minus, 37, equals, 0x 2 +14x−37=0 to the nearest tenth.

To solve the quadratic equation x^2 + 14x - 37 = 0, we can use the quadratic formula, which is x = [-b ± sqrt(b^2 - 4ac)] / (2a). In this equation, a = 1, b = 14, and c = -37.

Step 1: Calculate the value under the square root, which is b^2 - 4ac = (14)^2 - 41(-37) = 196 + 148 = 344.

Step 2: Calculate the square root of 344, which is approximately 18.55.

Step 3: Substitute these values into the quadratic formula to find the two possible values for x.

x = [-14 ± 18.55] / (2*1)

So, the two possible solutions are:

x = (-14 + 18.55) / 2 = 2.275 ≈ 2.3 (to the nearest tenth)

x = (-14 - 18.55) / 2 = -16.275 ≈ -16.3 (to the nearest tenth)

So, the solutions to the equation x^2 + 14x - 37 = 0 are x = 2.3 and x = -16.3 (to the nearest tenth).