4x^2-5x-33=-29 solve and round to the nearest tenth
4x^2-5x-33 = -29
4x^2-5x-4 = 0
Now solve as usual. I suggest the quadratic formula
To solve the quadratic equation 4x^2 - 5x - 33 = -29 and round to the nearest tenth, follow these steps:
Step 1: Begin by moving all terms to one side of the equation, bringing -29 to the left side:
4x^2 - 5x - 33 + 29 = 0
Simplifying the equation further:
4x^2 - 5x - 4 = 0
Step 2: We can use the quadratic formula to solve for x, which is given by:
x = (-b ± √(b^2 - 4ac))/2a
In our equation, a = 4, b = -5, and c = -4.
Substituting the values into the quadratic formula:
x = (-(-5) ± √((-5)^2 - 4 * 4 * (-4))) / (2 * 4)
Simplifying further:
x = (5 ± √(25 + 64)) / 8
x = (5 ± √(89)) / 8
Step 3: Since we need to round to the nearest tenth, we can use a calculator to evaluate the square root of 89, which is approximately 9.48683.
Plugging this value back into the equation:
x = (5 ± 9.48683) / 8
Calculating the two possible solutions:
x1 = (5 + 9.48683) / 8 ≈ 1.1861
x2 = (5 - 9.48683) / 8 ≈ -0.4361
Rounded to the nearest tenth, the solutions are:
x1 ≈ 1.2
x2 ≈ -0.4
Therefore, the solutions to the quadratic equation 4x^2 - 5x - 33 = -29, rounded to the nearest tenth, are x ≈ 1.2 and x ≈ -0.4.