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# Module 17

### Solving Equations by the Quadratic Formula and Quadratic Methods

QuestionAnswer
Solve x^2 - 8x + 14 = 0 using quadratic formula Use quadratic formula a = 1, b = -8, c = 14[x = -(-8)+/-√((-8)^2 -4(1)(4))/2(1)]. Use order of operations to simplify the quadratic formula[x=(8+/-√(64-56))/2 = (8+/-√8)/2]. Simplify the radical [x=(8+/-2√2)/2]. Reduce the problem[x=4+/-√2].
Solve -3x^2 +6x=-5 using quadratic formula Move 5 onto other side to make it equal to 0. Use quadratic formula[(-6+/-√6^2 -4(-3)(5))/2(-3)]. Use order of operations to simplify[(-6+/-√96)/-6]. Simplify the radical[(-6+/-4√6)/-6]. Reduce the problem[x=(3+/-2√6)/3].
Solve 2x^2 = 7x + 6 using quadratic formula Move 7x and 6 onto left side to make it equal to 0. Use quadratic formula [(-(-7)+/-√(-7)^2 -4(2)(-6))/2(2)]. Use order of operations to simplify[(7+/-√97)/4]. Simplify the radical, if you can. You can't in this problem, so the answer is x=(7+/-√97)/4.
Solve 3x^2 + 8 = -4x using quadratic formula Move -4x onto left side.Use quadratic formula[(-4+/-√462 -4(3)(8))/2(3)]. Simplify[(-4+/-√-80)/6]. Simplify radical, the root of a (-) # makes an imaginary #[(-4+/-4i√5)/6]. Complex #, so it must be written in a + bi form [-2/3 +/-(2√5)/3i].
Solve 6x^2 - 13x = 8 using quadratic formula Set equal to 0. Plug a,b,and c into quadratic formula. Use order of operations to simplify[(13+/-√361)/12]. Simplify the radical[(13+/-19)12]. No square roots, so solve for x. x=(13+19)/12 or (13-19)/12. x=8/3 or x=-1/2.
Solve x^2 + 5x = 24 using quadratic factoring method Write equation equal to 0[x^2 +5x-24=0]. Factor[(x+8)(x-3)=0]. Use Zero Product Property[x+8=0 or x-3=0]. Solve each equation[x=-8 or x=3].
Solve 9x^2 + 12 = 3 + 12x + 5x^2 using quadratic factoring method Write equation in standard form[4x^2 -12x+9=0]. Factor[(2x-3)(2x-3)=0]. Use Zero Product Property[2x-3=0]. Solve [x=3/2].
Solve x^2 - 16 = 0 using quadratic square root property method Get the perfect square on one side and the constant on the other side[x^2=16]. Use square root property to find square root of each side[√x^2=+/-√16]. Solve [x=+/-4].
Solve (x+1)^2 = 49 using quadratic square root property method Make sure there is a perfect square on one side and a constant on the other. Use the square root property to find the square root of each side[√(x+1)^2=+/-√49]. Solve[x+1=7 or x+1=-7] x=6 or x=-8
Solve x^2 + 12x + 2 = 0 using quadratic completing the square method Move constant to other side[x^2 +12x=-2]. Complete the square[x^2 +12x+36=-2+36<---{(12/2)^2=36}, (x+6)^2=34]. Use square root property[√(x+6)2=+/-√34, x+6=+/-√34]. Solve each resulting equation[x = -6+/-√34].
Created by: ibrahim2747