Solve the equation 3x^(2)-18 x+23=x^(2)-10 to the nearest tenth. Answer: x=

Combine and Rearrange Terms: First, we need to combine like terms and move all terms to one side of the equation to set it equal to zero. 3x^2 - 18x + 23 = x^2 - 10 Subtract x^2 from both sides and add 10 to both sides to get: 3x^2 - x^2 - 18x + 23 + 10 = 0Combine Like Terms: Now, combine like terms. (3x^2 - x^2) - 18x + (23 + 10) = 0 2x^2 - 18x + 33 = 0Solve Quadratic Equation: Next, we need to solve the quadratic equation 2x^2 - 18x + 33 = 0. We can use the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / (2a), where a = 2, b = -18, and c = 33. First, calculate the discriminant (b^2 - 4ac): (-18)^2 - 4(2)(33) = 324 - 264 = 60Calculate Discriminant: Now, plug the values into the quadratic formula: x = [-(-18) ± sqrt(60)] / (2 * 2) x = [18 ± sqrt(60)] / 4Apply Quadratic Formula: Simplify the square root and the fraction: x = [18 ± 7.746] / 4 We will have two solutions for x: x1 = (18 + 7.746) / 4 x2 = (18 - 7.746) / 4Calculate Solutions: Calculate the two possible values for x: x1 = 25.746 / 4 x1 ≈ 6.4 (to the nearest tenth) x2 = 10.254 / 4 x2 ≈ 2.6 (to the nearest tenth)

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve the equation
3x^(2)-18 x+23=x^(2)-10 to the nearest tenth.
Answer:
x=

Solve the equation $3 x^{2}-18 x+23=x^{2}-10$ to the nearest tenth. $\newline$ Answer: $x=$

View step-by-step help

Home

Math Problems

Algebra 1

Solve linear equations: mixed review

Full solution

Q. Solve the equation

3 x^{2}-18 x+23=x^{2}-10

to the nearest tenth.

\newline

Answer:

x=

Combine and Rearrange Terms: First, we need to combine like terms and move all terms to one side of the equation to set it equal to zero. $\newline$ $3x^2 - 18x + 23 = x^2 - 10$ $\newline$ Subtract $x^2$ from both sides and add $10$ to both sides to get: $\newline$ $3x^2 - x^2 - 18x + 23 + 10 = 0$
Combine Like Terms: Now, combine like terms. $\newline$ $(3x^2 - x^2) - 18x + (23 + 10) = 0$ $\newline$ $2x^2 - 18x + 33 = 0$
Solve Quadratic Equation: Next, we need to solve the quadratic equation $2x^2 - 18x + 33 = 0$ . We can use the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ , where $a = 2$ , $b = -18$ , and $c = 33$ . First, calculate the discriminant ( $b^2 - 4ac$ ): $(-18)^2 - 4(2)(33) = 324 - 264 = 60$
Calculate Discriminant: Now, plug the values into the quadratic formula: $\newline$ $x = \frac{-(-18) \pm \sqrt{60}}{2 \cdot 2}$ $\newline$ $x = \frac{18 \pm \sqrt{60}}{4}$
Apply Quadratic Formula: Simplify the square root and the fraction: $\newline$ $x = \frac{18 \pm 7.746}{4}$ $\newline$ We will have two solutions for $x$ : $\newline$ $x_1 = \frac{18 + 7.746}{4}$ $\newline$ $x_2 = \frac{18 - 7.746}{4}$
Calculate Solutions: Calculate the two possible values for $x$ : $x_1 = \frac{25.746}{4}$ $x_1 \approx 6.4$ (to the nearest tenth) $x_2 = \frac{10.254}{4}$ $x_2 \approx 2.6$ (to the nearest tenth)