give exact and approximate solutions to three decimal places. x^2+5x-7=0

using the quadratic formula,

x = [-5 +/- sqrt(25+28)]/2
= -6.140 or 1.140

To find the solutions to the quadratic equation x^2 + 5x - 7 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac))/(2a)

In this equation, a = 1, b = 5, and c = -7. Plugging these values into the quadratic formula, we get:

x = (-(5) ± √((5)^2 - 4(1)(-7)))/(2(1))

Simplifying further:

x = (-5 ± √(25 + 28))/2

x = (-5 ± √(53))/2

Therefore, the exact solutions to the quadratic equation are:

x = (-5 + √(53))/2 and x = (-5 - √(53))/2

Approximating these solutions to three decimal places, we get:

x ≈ 0.792 and x ≈ -5.792

To find the exact and approximate solutions to the quadratic equation x^2 + 5x - 7 = 0, we can use the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / (2a),

where a, b, and c are the coefficients of the quadratic equation.

Comparing the equation x^2 + 5x - 7 = 0 with the general quadratic equation form ax^2 + bx + c = 0, we can deduce:

a = 1, b = 5, and c = -7.

Now, substitute these values into the quadratic formula:

x = (-(5) ± sqrt(5^2 - 4(1)(-7))) / (2(1)).

Simplifying further:

x = (-5 ± sqrt(25 + 28)) / 2.

x = (-5 ± sqrt(53)) / 2.

Therefore, the exact solutions are:

x = (-5 + sqrt(53)) / 2,

x = (-5 - sqrt(53)) / 2.

To find the approximate solutions to three decimal places, we can use a calculator to evaluate these expressions:

x ≈ (-5 + sqrt(53)) / 2 ≈ 0.712,

x ≈ (-5 - sqrt(53)) / 2 ≈ -5.712.

Hence, the exact solutions are (-5 ± sqrt(53)) / 2, and the approximate solutions to three decimal places are approximately 0.712 and -5.712.