Math Problem Statement

Solve the following algebraic equations: 1) |7 - x| = -7 2) |x + 6| = x + 10 3) √((x - 9)^2) = x - 9 4) x^2 - 12x + 11 = 0 5) x^2 - 15x + 56 = 0 6) 6x^2 + 7x - 3 = 0 7) 16x^2 + 8x + 1 = 0 8) x^4 - 10x^2 + 9 = 0 9) 10x^4 + 7x^2 + 1 = 0

Solution

The image contains a list of algebraic equations with the instruction to solve them. Here is a transcription of the exercises:

12. Solve the equation:

  1. 7x=7|7 - x| = -7

  2. x+6=x+10|x + 6| = x + 10

  3. (x9)2=x9\sqrt{(x - 9)^2} = x - 9


13. Solve the equation:

  1. x212x+11=0x^2 - 12x + 11 = 0

  2. x215x+56=0x^2 - 15x + 56 = 0

  3. 6x2+7x3=06x^2 + 7x - 3 = 0

  4. 16x2+8x+1=016x^2 + 8x + 1 = 0


14. Solve the equation:

  1. x410x2+9=0x^4 - 10x^2 + 9 = 0

  2. 10x4+7x2+1=010x^4 + 7x^2 + 1 = 0


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Math Problem Analysis

Mathematical Concepts

Absolute Value Equations
Square Root Functions
Quadratic Equations
Higher-Degree Polynomial Equations

Formulas

|a| = b
√((a)^2) = a
Quadratic Formula: x = [-b ± √(b² - 4ac)] / 2a

Theorems

Properties of Absolute Value
Properties of Square Roots
Quadratic Formula

Suitable Grade Level

Grades 9-11