Math / Algebra

QuestionQuestion Watch $v$
Solve the quadratic by factoring. $5 x^{2}-20 x+14=2 x+6$

Studdy Solution

STEP 1

1. The given equation is a quadratic equation.
2. We need to bring all terms to one side to set the equation to zero.
3. We will solve the quadratic equation by factoring.

STEP 2

1. Rearrange the equation to set it to zero.
2. Simplify the equation.
3. Factor the quadratic equation.
4. Solve for $x$ .

STEP 3

Rearrange the equation to bring all terms to one side. Subtract $2x$ and $6$ from both sides:
$5x^2 - 20x + 14 = 2x + 6$ $5x^2 - 20x + 14 - 2x - 6 = 0$

STEP 4

Simplify the equation by combining like terms:
$5x^2 - 22x + 8 = 0$

STEP 5

Factor the quadratic equation. Look for two numbers that multiply to $5 \times 8 = 40$ and add to $-22$ .
The numbers are $-20$ and $-2$ .
Rewrite the middle term using these numbers:
$5x^2 - 20x - 2x + 8 = 0$

STEP 6

Factor by grouping. Group the terms and factor out the greatest common factor from each group:
$(5x^2 - 20x) + (-2x + 8) = 0$ $5x(x - 4) - 2(x - 4) = 0$
Factor out the common factor $(x - 4)$ :
$(5x - 2)(x - 4) = 0$

STEP 7

Solve for $x$ by setting each factor equal to zero:
$5x - 2 = 0 \quad \text{or} \quad x - 4 = 0$
Solve each equation:
$5x - 2 = 0$ $5x = 2$ $x = \frac{2}{5}$
$x - 4 = 0$ $x = 4$
The solutions for $x$ are:
$x = \frac{2}{5} \quad \text{and} \quad x = 4$

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QuestionQuestion Watch $v$
Solve the quadratic by factoring. $5 x^{2}-20 x+14=2 x+6$

Studdy Solution

STEP 1

1. The given equation is a quadratic equation.
2. We need to bring all terms to one side to set the equation to zero.
3. We will solve the quadratic equation by factoring.

STEP 2

1. Rearrange the equation to set it to zero.
2. Simplify the equation.
3. Factor the quadratic equation.
4. Solve for $x$ .

STEP 3

Rearrange the equation to bring all terms to one side. Subtract $2x$ and $6$ from both sides:
$5x^2 - 20x + 14 = 2x + 6$ $5x^2 - 20x + 14 - 2x - 6 = 0$

STEP 4

Simplify the equation by combining like terms:
$5x^2 - 22x + 8 = 0$

STEP 5

Factor the quadratic equation. Look for two numbers that multiply to $5 \times 8 = 40$ and add to $-22$ .
The numbers are $-20$ and $-2$ .
Rewrite the middle term using these numbers:
$5x^2 - 20x - 2x + 8 = 0$

STEP 6

Factor by grouping. Group the terms and factor out the greatest common factor from each group:
$(5x^2 - 20x) + (-2x + 8) = 0$ $5x(x - 4) - 2(x - 4) = 0$
Factor out the common factor $(x - 4)$ :
$(5x - 2)(x - 4) = 0$

STEP 7

Solve for $x$ by setting each factor equal to zero:
$5x - 2 = 0 \quad \text{or} \quad x - 4 = 0$
Solve each equation:
$5x - 2 = 0$ $5x = 2$ $x = \frac{2}{5}$
$x - 4 = 0$ $x = 4$
The solutions for $x$ are:
$x = \frac{2}{5} \quad \text{and} \quad x = 4$

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QuestionQuestion Watch vvvSolve the quadratic by factoring. 5x2−20x+14=2x+65 x^{2}-20 x+14=2 x+65x2−20x+14=2x+6

Studdy Solution

STEP 1

1. The given equation is a quadratic equation.2. We need to bring all terms to one side to set the equation to zero.3. We will solve the quadratic equation by factoring.

STEP 2

1. Rearrange the equation to set it to zero.2. Simplify the equation.3. Factor the quadratic equation.4. Solve for x x x.

STEP 3

Rearrange the equation to bring all terms to one side. Subtract 2x 2x 2x and 6 6 6 from both sides:5x2−20x+14=2x+6 5x^2 - 20x + 14 = 2x + 6 5x2−20x+14=2x+6 5x2−20x+14−2x−6=0 5x^2 - 20x + 14 - 2x - 6 = 0 5x2−20x+14−2x−6=0

STEP 4

Simplify the equation by combining like terms:5x2−22x+8=0 5x^2 - 22x + 8 = 0 5x2−22x+8=0

STEP 5

Factor the quadratic equation. Look for two numbers that multiply to 5×8=40 5 \times 8 = 40 5×8=40 and add to −22-22−22.The numbers are −20-20−20 and −2-2−2.Rewrite the middle term using these numbers:5x2−20x−2x+8=0 5x^2 - 20x - 2x + 8 = 0 5x2−20x−2x+8=0

STEP 6

STEP 7

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QuestionQuestion Watch $v$
Solve the quadratic by factoring. $5 x^{2}-20 x+14=2 x+6$

1. The given equation is a quadratic equation.
2. We need to bring all terms to one side to set the equation to zero.
3. We will solve the quadratic equation by factoring.

1. Rearrange the equation to set it to zero.
2. Simplify the equation.
3. Factor the quadratic equation.
4. Solve for $x$ .

Rearrange the equation to bring all terms to one side. Subtract $2x$ and $6$ from both sides:
$5x^2 - 20x + 14 = 2x + 6$ $5x^2 - 20x + 14 - 2x - 6 = 0$

Simplify the equation by combining like terms:
$5x^2 - 22x + 8 = 0$

Factor the quadratic equation. Look for two numbers that multiply to $5 \times 8 = 40$ and add to $-22$ .
The numbers are $-20$ and $-2$ .
Rewrite the middle term using these numbers:
$5x^2 - 20x - 2x + 8 = 0$