Solve Quadratic Equation for 4b^2+20b+25=169

Publish date: 2024-05-18
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Solve the quadratic:

4b2+20b+25 = 169

The quadratic you entered is not in standard form:
ax2 + bx + c = 0

Subtract 169 from both sides
4b2+20b+25 - 169 = 169 - 169
Simplifying, we get:
4b2+20b-144 = 0
Set up the a, b, and c values:

a = 4, b = 20, c = -144

Quadratic Formula
b  =  -b ± √b2 - 4ac
  2a

Calculate -b

-b = -(20)

-b = -20

Calculate the discriminant Δ

Δ = b2 - 4ac:

Δ = 202 - 4 x 4 x -144

Δ = 400 - -2304

Δ = 2704 <--- Discriminant

Since Δ > 0, we expect two real roots.

Take the square root of Δ

√Δ = √(2704)

√Δ = 52

-b + Δ:

Numerator 1 = -b + √Δ

Numerator 1 = -20 + 52

Numerator 1 = 32

-b - Δ:

Numerator 2 = -b - √Δ

Numerator 2 = -20 - 52

Numerator 2 = -72

Calculate 2a

Denominator = 2 * a

Denominator = 2 * 4

Denominator = 8

Find Solutions
Solution 1  =  Numerator 1
  Denominator

Solution 1  =  32
  8

Solution 1 = 4

Solution 2
Solution 2  =  Numerator 2
  Denominator

Solution 2  =  -72
  8

Solution 2 = -9

Solution Set

(Solution 1, Solution 2) = (4, -9)

Prove our first answer

(4)2 + 20(4) - 144 ? 0

(16) + 80144 ? 0

64 + 80144 ? 0

0 = 0

Prove our second answer

(-9)2 + 20(-9) - 144 ? 0

(81) - 180144 ? 0

324 - 180144 ? 0

0 = 0

Final Answer

(Solution 1, Solution 2) = (4, -9)

You have 1 free calculations remaining


What is the Answer?

(Solution 1, Solution 2) = (4, -9)

How does the Quadratic Equations and Inequalities Calculator work?

Free Quadratic Equations and Inequalities Calculator - Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
This calculator has 4 inputs.

What 5 formulas are used for the Quadratic Equations and Inequalities Calculator?

y = ax2 + bx + c
(-b ± √b2 - 4ac)/2a
h (Axis of Symmetry) = -b/2a
The vertex of a parabola is (h,k) where y = a(x - h)2 + k

For more math formulas, check out our Formula Dossier

What 9 concepts are covered in the Quadratic Equations and Inequalities Calculator?

complete the squarea technique for converting a quadratic polynomial of the form ax2 + bx + c to a(x - h)2 + kequationa statement declaring two mathematical expressions are equalfactora divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n.interceptparabolaa plane curve which is approximately U-shapedquadraticPolynomials with a maximum term degree as the second degreequadratic equations and inequalitiesrational rootvertexHighest point or where 2 curves meet

Example calculations for the Quadratic Equations and Inequalities Calculator

Quadratic Equations and Inequalities Calculator Video


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