Question

1. solve for x:

-49 + 16x² = 0
-64 + 9x² = 0

1. simplify:

(3x² - 4x + 9) - (2x² - 9x + 12)
(24x³ + 6x - 3) + (5x³ - 9x + 7)
(10x² - 8x + 13) - (2x² - 9x + 2)

Explanation:

Problem 15: Solve for $x$

Step1: Rearrange first equation

$16x^2 = 49$

Step2: Isolate $x^2$

$x^2 = \frac{49}{16}$

Step3: Solve for $x$

$x = \pm\sqrt{\frac{49}{16}} = \pm\frac{7}{4}$

Step4: Rearrange second equation

$9x^2 = 64$

Step5: Isolate $x^2$

$x^2 = \frac{64}{9}$

Step6: Solve for $x$

$x = \pm\sqrt{\frac{64}{9}} = \pm\frac{8}{3}$

Expression 1: Distribute the negative sign

$(3x^2 - 4x + 9) - (2x^2 - 9x + 12) = 3x^2 - 4x + 9 - 2x^2 + 9x - 12$

Expression 1: Combine like terms

$(3x^2-2x^2)+(-4x+9x)+(9-12) = x^2 + 5x - 3$

Expression 2: Remove parentheses

$(24x^3 + 6x - 3) + (5x^3 - 9x + 7) = 24x^3 + 6x - 3 + 5x^3 - 9x + 7$

Expression 2: Combine like terms

$(24x^3+5x^3)+(6x-9x)+(-3+7) = 29x^3 - 3x + 4$

Expression 3: Distribute the negative sign

$(10x^2 - 8x + 13) - (2x^2 - 9x + 2) = 10x^2 - 8x + 13 - 2x^2 + 9x - 2$

Expression 3: Combine like terms

$(10x^2-2x^2)+(-8x+9x)+(13-2) = 8x^2 + x + 11$

Answer:

For $-49 + 16x^2 = 0$: $x = \frac{7}{4}$ or $x = -\frac{7}{4}$
For $-64 + 9x^2 = 0$: $x = \frac{8}{3}$ or $x = -\frac{8}{3}$

---

Problem 16: Simplify