Let’s solve each quadratic equation by factoring. We’ll move all terms to one side so the equation equals zero, then factor the quadratic expression and set each factor equal to zero.
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1.) 4x² + 16x = 48
Step 1: Move 48 to left → 4x² + 16x - 48 = 0
Step 2: Factor out GCF (4) → 4(x² + 4x - 12) = 0
Step 3: Factor trinomial → x² + 4x - 12 = (x + 6)(x - 2)
So: 4(x + 6)(x - 2) = 0
Step 4: Set factors to zero → x + 6 = 0 or x - 2 = 0
→ x = -6 or x = 2
✔ Check:
If x = -6: 4(36) + 16(-6) = 144 - 96 = 48 ✔️
If x = 2: 4(4) + 16(2) = 16 + 32 = 48 ✔️
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2.) x² + 7x = -6
Step 1: Move -6 to left → x² + 7x + 6 = 0
Step 2: Factor → (x + 1)(x + 6) = 0
Step 3: Set factors to zero → x = -1 or x = -6
✔ Check:
x = -1: 1 -7 = -6 ✔️
x = -6: 36 - 42 = -6 ✔️
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3.) x² + 13x = -42
Step 1: Move -42 → x² + 13x + 42 = 0
Step 2: Factor → (x + 6)(x + 7) = 0
→ x = -6 or x = -7
✔ Check:
x = -6: 36 - 78 = -42 ✔️
x = -7: 49 - 91 = -42 ✔️
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4.) x² + 6 = 5x
Step 1: Move 5x → x² - 5x + 6 = 0
Step 2: Factor → (x - 2)(x - 3) = 0
→ x = 2 or x = 3
✔ Check:
x=2: 4+6=10, 5*2=10 ✔️
x=3: 9+6=15, 5*3=15 ✔️
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5.) 8x² + 80 = -56x
Step 1: Move -56x → 8x² + 56x + 80 = 0
Step 2: Factor out GCF (8) → 8(x² + 7x + 10) = 0
Step 3: Factor → (x + 2)(x + 5) = 0
→ x = -2 or x = -5
✔ Check:
x=-2: 8(4)+80=32+80=112; -56*(-2)=112 ✔️
x=-5: 8(25)+80=200+80=280; -56*(-5)=280 ✔️
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6.) x² = -x + 2
Step 1: Move all to left → x² + x - 2 = 0
Step 2: Factor → (x + 2)(x - 1) = 0
→ x = -2 or x = 1
✔ Check:
x=-2: 4 = 2+2=4 ✔️
x=1: 1 = -1+2=1 ✔️
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7.) 2x² + 84 = 26x
Step 1: Move 26x → 2x² - 26x + 84 = 0
Step 2: Factor out GCF (2) → 2(x² - 13x + 42) = 0
Step 3: Factor → (x - 6)(x - 7) = 0
→ x = 6 or x = 7
✔ Check:
x=6: 2(36)+84=72+84=156; 26*6=156 ✔️
x=7: 2(49)+84=98+84=182; 26*7=182 ✔️
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8.) x² = 6x - 5
Step 1: Move all → x² - 6x + 5 = 0
Step 2: Factor → (x - 1)(x - 5) = 0
→ x = 1 or x = 5
✔ Check:
x=1: 1 = 6-5=1 ✔️
x=5: 25 = 30-5=25 ✔️
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9.) x² - 3x = 40
Step 1: Move 40 → x² - 3x - 40 = 0
Step 2: Factor → (x - 8)(x + 5) = 0
→ x = 8 or x = -5
✔ Check:
x=8: 64 - 24 = 40 ✔️
x=-5: 25 +15 = 40 ✔️
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10.) 4x² + 168 = 52x
Step 1: Move 52x → 4x² - 52x + 168 = 0
Step 2: Factor out GCF (4) → 4(x² - 13x + 42) = 0
Step 3: Factor → (x - 6)(x - 7) = 0
→ x = 6 or x = 7
✔ Check:
x=6: 4(36)+168=144+168=312; 52*6=312 ✔️
x=7: 4(49)+168=196+168=364; 52*7=364 ✔️
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Final Answer:
1.) x = -6, 2
2.) x = -1, -6
3.) x = -6, -7
4.) x = 2, 3
5.) x = -2, -5
6.) x = -2, 1
7.) x = 6, 7
8.) x = 1, 5
9.) x = 8, -5
10.) x = 6, 7
Parent Tip: Review the logic above to help your child master the concept of factoring trinomials worksheet.
