Question

5x^2+ 15x – 140 = 0 Solve for x

Answer 1

Answer:

x = 4, -7

Step-by-step explanation:

1) Factor out the common term 5.

$5( {x}^{2} + 3x - 28) = 0$

2) Factor x² + 3x - 28.

$5(x - 4)(x + 7) = 0$

3) Solve for x.

x = 4, -7

Therefor, the answer is x = 4, -7.

Answer 2

Answer:

x = 4, -7

Step-by-step explanation:

1. Solve the equation using the quadratic formula

The Quadratic formula provides the solution for $Ax^{2} +Bx+C=0$

in which A, B, and C are numbers (or coefficients), as follows:

$\frac{-b+\sqrt{b^{2}-4ac } }{2a}$

2. Determine the quadratic equation’s coefficients A, B, and C

The coefficients of our equation, $5x^{2} +15x-140=0$, are:

A = 5

B = 15

C = -140

3. Plug these coefficients into the quadratic formula

$\frac{-b+\sqrt{b^{2}-4ac } }{2a}=\frac{-15+\sqrt{15^{2}-4x5x-140 } }{2x5}$

Calculate the expression inside the parentheses.

Simplify exponents and square roots.

$\frac{-15+\sqrt{15^{2}-4x5x-140 } }{2x5}$

$\frac{-15+\sqrt{225-4x5x-140 } }{2x5}$

Perform any multiplication or division, from left to right.

$\frac{-15+\sqrt{225-20x-140 } }{2x5}$

$\frac{-15+\sqrt{225-2800 } }{2x5}$

$\frac{-15+\sqrt{3025} }{2x5}$

$\frac{-15+\sqrt{3025} }{10}$

to get the result:

$x=\frac{-15+\sqrt{3025} }{10}$

4. Simplify square root

Simplify 3025 by finding its prime factors.

                    3025

                   /         \

                 /             \

             5                  605

              /                    \

            /                        \

          5                          "121"

           /                            \

         /                                \

        11                                11

The prime factorization of 3025 is 5² • 11²

Write the prime factors.

$\sqrt{3025}$ = √5 • 5 • 11 • 11

Group the prime factors into pairs and rewrite in exponent form.

√5 • 5 • 11 • 11 = $\sqrt{5^{2}x11^{2} }$

Use rule $\sqrt{x^{2} }$ = x to simplify futher.

$\sqrt{5^{2}x11^{2}}$ = 5 • 11

5 • 11 = 55

5. Solve the equation for x

x = $\frac{-15+55}{10}$

The ± means two answers are possible:

x = 4

or

x = - 7