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Step by step

1. Start from the quadratic formula

   x = −b ± b2 − 4ac2a
2. Substitute a, b and c

   x = −(−2) ± (−2)2 − 4(1)(−15)2(1)
3. Work out the discriminant, b² − 4ac

   Δ = (−2)2 − 4(1)(−15) = 64
4. The discriminant is a perfect square, so the roots are rational

   64 = 8
5. Take the plus branch

   x₁ = 2 + 82 = 5
6. Take the minus branch

   x₂ = 2 − 82 = −3

Also worth knowing

Vertex

(1, −16)

Axis of symmetry

x = 1

Discriminant

64

Parabola opens

upward

Factored form

(x − 5)(x + 3) = 0

Step by step

1. The problem

   12+13
2. Find the least common denominator of 2 and 3

   LCD = 6
3. Rewrite both fractions over that denominator

   12 = 3613 = 26
4. Add the numerators

   3 + 26 = 56
5. The result is already in lowest terms

   gcd(5, 6) = 1

Step by step

1. Copy the first two columns to the right of the matrix

   22−5223153172.2672.2
2. Multiply along the three diagonals going down-right, and add them

   2 × 1 × 6 + 2 × 5 × 7 + (−5) × 3 × 2.2
3. That gives the positive part of the determinant

   12 + 70 + −33 = 49
4. Multiply along the three diagonals going up-right, and add them

   7 × 1 × (−5) + 2.2 × 5 × 2 + 6 × 3 × 2
5. That gives the part to be subtracted

   −35 + 22 + 36 = 23
6. Subtract the second sum from the first

   det = 49 − 23 = 26

Step by step

1. Give each digit its place value — powers of 2, right to left

   1×27 + 1×26 + 0×25 + 1×24 + 0×23 + 1×22 + 1×21 + 0×20
2. Work out each term

   128 + 64 + 0 + 16 + 0 + 4 + 2 + 0
3. Add them up

   110101102 = 21410

Step by step

1. Multiply width by height

   A = w × h = 12 × 7 = 84
2. Add both pairs of sides

   P = 2(w + h) = 2(12 + 7) = 38

Step by step

1. Set the two ratios equal to each other

   100250 = 15x
2. Cross multiply

   100 × x = 250 × 15
3. Divide both sides by A to isolate x

   x = 250 × 15100 = 3750100
4. Work out the division

   x = 37.5