Complete the Square for x^2+2x=35

Publish date: 2024-06-16
Complete the Square for x^2+2x=35

Complete the Square for x^2+2x=35

Image to Crop Complete the square for the quadratic
x2+2x = 35

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

Subtract 35 from both sides

x2+2x - 35 = 35 - 35
x2+2x - 35 = 0

We have our a, b, and c values:
a = 1, b = 2, c = -35

Complete the square for
x2 + 2x - 35=

Add 35 to each side
x2 + 2x - 35= + 35 = 0 + 35
x2x = 35

Complete the square:

Add an amount to both sides
x2 + 2x + ? = 35 + ?
Add (½*middle coefficient)2 to each side
Amount to add  =  (1 x 2)2
  (2 x 1)2

Amount to add  =  (2)2
  (2)2

Amount to add  =  4
  4

Amount to add = 4/4

Rewrite our perfect square equation:

x2 + 2 + (2/2)2 = 35 + (2/2)2
(x + 2/2)2 = 35 + 4/4

Simplify Right Side of the Equation:

LCM of 1 and 4 = 4

We multiply 35 by 4 ÷ 1 = 4 and 4 by 4 ÷ 4 = 1

Simplified Fraction  =  35 x 4 + 4 x 1
  4

Simplified Fraction  =  140 + 4
  4

Simplified Fraction  =  144
  4

Simplified Fraction = 36

We set our left side = u
u2 = (x + 2/2)2

u has two solutions:

u = +√36
u = -√36

Replacing u, we get:

x + 2/2 = +6
x + 2/2 = -6

Subtract 2/2 from the both sides

x + 2/2 - 2/2 = +6/1 - 2/2

Simplify right side of the equation

LCM of 1 and 2 = 2

We multiply 6 by 2 ÷ 1 = 2 and -2 by 2 ÷ 2 = 1

Simplified Fraction  =  6 x 2 - 2 x 1
  2

Simplified Fraction  =  12 - 2
  2

Simplified Fraction  =  10
  2

Simplified Fraction = 5

Answer 1 = 5

Subtract 2/2 from the both sides

x + 2/2 - 2/2 = -6/1 - 2/2

Simplify right side of the equation

LCM of 1 and 2 = 2

We multiply -6 by 2 ÷ 1 = 2 and -2 by 2 ÷ 2 = 1

Simplified Fraction  =  -6 x 2 - 2 x 1
  2

Simplified Fraction  =  -12 - 2
  2

Simplified Fraction  =  -14
  2

Simplified Fraction = -7

Answer 2 = -7


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

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