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# Solving Equations

### Solving equations by quadratic formula and quadratic method

Question | Answer |
---|---|

What is the quadratic formula? How many solutions will you get? | x = [ -b ± sqrt(b^2 - 4ac) ] / 2a 2 solutions |

What is the first step when solving a quadratic equation? | Write equation in standard form ax^2+bx+c=0 |

Is 3x^2+10=25 in standard form? If not, make corrections. | -No this equation is not in standard form and does not equal 0 -subtract 25 from both sides 3x^2+10-25=0 is correct form |

Identify values for a,b, & c in this equation? 3x^2 + 10x - 25 = 0 | a=3 b=10 c=-25 |

Identify values for a,b, & c in this equation? x^2 - 4x + 9 = 0 | a=1 b=-4 c=9 |

Solve for x using the quadratic formula for this equation: x^2 + 2x - 8 = 0 | Identify values for a,b, & c. Plug a=1, b=2,c=-8 into the quadratic formula and simplify. x = [ -2 ± sqrt(2^2 - 4(1)(-8) ] / 2(1) x = [-2 ± sqrt (4+32) ] / 2 x = [-2 ± sqrt (36) ] / 2 [Look for a perfect square factor] x = -2 ± 6 / 2 x = -4, x = 2 |

What part of the quadratic formula is called the discriminant and what is this used for? | b^2 - 4ac to determine the type of solutions produced by the equation |

When using the discriminant, what type of solutions will a positive, negative and an answer of 0 produce? | positive = two real solutions 0 = one real solution negative = two complex but not real solutions |

How would you solve for x with a triangle that has a known hypotenuse of 36 and one side that is 8 feet longer than the last side? | Use the equation x^2 + (x+8)^2 = 36^2 Simplify, combine like terms, and set equation = 0 2x^2+16x-1232=0 (Factoring out 2 optional) Plug in values into quadratic formula & simply Only use positive answer for solution for distance (x=about 21) |

In a equation like (p+2)^2 = 9(p+2) - 20, you can substitute (p+2) with x to make the equation less intimidating. Try to solve. | x^2 = 9x - 20 Write in standard form, factor or use quadratic equation (x-4)(x-5)=0 set each value equal to 0 and solve x=4, x=5 plug x values into x=p+2 & solve for p since we used substitution p=2, p=3. Plug p values back into original equation |