Solve the equation 2x^(2)-15 x+20=0 to the nearest tenth. Answer: x=

Use Quadratic Formula: We will use the quadratic formula to solve the equation 2x^2 - 15x + 20 = 0. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients from the quadratic equation ax^2 + bx + c = 0. In our case, a = 2, b = -15, and c = 20.Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: b^2 - 4ac. Discriminant = (-15)^2 - 4 * 2 * 20 = 225 - 160 = 65.Plug Values and Solve: Now we can plug the values of a, b, and the discriminant into the quadratic formula to find the two possible values for x. x = (-(-15) ± √65) / (2 * 2) x = (15 ± √65) / 4Calculate First Solution: We will now calculate the two possible solutions for x. First solution: x = (15 + √65) / 4 Second solution: x = (15 - √65) / 4Calculate Second Solution: Let's calculate the first solution: x = (15 + √65) / 4 x ≈ (15 + 8.062) / 4 x ≈ 23.062 / 4 x ≈ 5.7655 Rounded to the nearest tenth, x ≈ 5.8Now, let's calculate the second solution: x = (15 - √65) / 4 x ≈ (15 - 8.062) / 4 x ≈ 6.938 / 4 x ≈ 1.7345 Rounded to the nearest tenth, x ≈ 1.7

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation
2x^(2)-15 x+20=0 to the nearest tenth.
Answer:
x=

Solve the equation $2 x^{2}-15 x+20=0$ to the nearest tenth. $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Algebra 2

Solve exponential equations using common logarithms

Full solution

Q. Solve the equation

2 x^{2}-15 x+20=0

to the nearest tenth.

\newline

Answer:

x=

Use Quadratic Formula: We will use the quadratic formula to solve the equation $2x^2 - 15x + 20 = 0$ . The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a$ , $b$ , and $c$ are the coefficients from the quadratic equation $ax^2 + bx + c = 0$ . In our case, $a = 2$ , $b = -15$ , and $c = 20$ .
Calculate Discriminant: First, we calculate the discriminant, which is the part under the square root in the quadratic formula: $b^2 - 4ac$ . Discriminant = $(-15)^2 - 4 \times 2 \times 20 = 225 - 160 = 65$ .
Plug Values and Solve: Now we can plug the values of $a$ , $b$ , and the discriminant into the quadratic formula to find the two possible values for $x$ . $\newline$ $x = \frac{-(-15) \pm \sqrt{65}}{2 \times 2}$ $\newline$ $x = \frac{15 \pm \sqrt{65}}{4}$
Calculate First Solution: We will now calculate the two possible solutions for $x$ . $\newline$ First solution: $x = \frac{15 + \sqrt{65}}{4}$ $\newline$ Second solution: $x = \frac{15 - \sqrt{65}}{4}$
Calculate Second Solution: Let's calculate the first solution: $\newline$ $x = \frac{15 + \sqrt{65}}{4}$ $\newline$ $x \approx \frac{15 + 8.062}{4}$ $\newline$ $x \approx \frac{23.062}{4}$ $\newline$ $x \approx 5.7655$ $\newline$ Rounded to the nearest tenth, $x \approx 5.8$
Calculate Second Solution: Let's calculate the first solution: $\newline$ $x = \frac{15 + \sqrt{65}}{4}$ $\newline$ $x \approx \frac{15 + 8.062}{4}$ $\newline$ $x \approx \frac{23.062}{4}$ $\newline$ $x \approx 5.7655$ $\newline$ Rounded to the nearest tenth, $x \approx 5.8$ Now, let's calculate the second solution: $\newline$ $x = \frac{15 - \sqrt{65}}{4}$ $\newline$ $x \approx \frac{15 - 8.062}{4}$ $\newline$ $x \approx \frac{6.938}{4}$ $\newline$ $x \approx 1.7345$ $\newline$ Rounded to the nearest tenth, $x \approx 1.7$