Question Solve the equation $-4 x = 16 x^{2}$ for $x$ .

Studdy Solution

STEP 1

1. The equation $-4x = 16x^2$ is a quadratic equation in standard form.
2. The solutions can be found by factoring, completing the square, or using the quadratic formula.
3. The variable $x$ represents a real number.

STEP 2

1. Rearrange the equation to standard quadratic form.
2. Factor the quadratic expression.
3. Solve for $x$ by setting each factor equal to zero.

STEP 3

Rearrange the equation to standard quadratic form by moving all terms to one side of the equation.
$16x^2 + 4x = 0$

STEP 4

Factor out the common factor from the quadratic expression.
$x(16x + 4) = 0$

STEP 5

Further factor the expression by factoring out the common factor of 4 in the second term.
$x(4(4x + 1)) = 0$

STEP 6

Set each factor equal to zero to solve for $x$ .
$x = 0 \quad \text{and} \quad 4(4x + 1) = 0$

STEP 7

Solve the second equation for $x$ .
$4x + 1 = 0$ $4x = -1$ $x = -\frac{1}{4}$

STEP 8

Combine the solutions from both factors.
The solutions are $x = 0$ and $x = -\frac{1}{4}$ .

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Question Solve the equation $-4 x = 16 x^{2}$ for $x$ .

Studdy Solution

STEP 1

1. The equation $-4x = 16x^2$ is a quadratic equation in standard form.
2. The solutions can be found by factoring, completing the square, or using the quadratic formula.
3. The variable $x$ represents a real number.

STEP 2

1. Rearrange the equation to standard quadratic form.
2. Factor the quadratic expression.
3. Solve for $x$ by setting each factor equal to zero.

STEP 3

Rearrange the equation to standard quadratic form by moving all terms to one side of the equation.
$16x^2 + 4x = 0$

STEP 4

Factor out the common factor from the quadratic expression.
$x(16x + 4) = 0$

STEP 5

Further factor the expression by factoring out the common factor of 4 in the second term.
$x(4(4x + 1)) = 0$

STEP 6

Set each factor equal to zero to solve for $x$ .
$x = 0 \quad \text{and} \quad 4(4x + 1) = 0$

STEP 7

Solve the second equation for $x$ .
$4x + 1 = 0$ $4x = -1$ $x = -\frac{1}{4}$

STEP 8

Combine the solutions from both factors.
The solutions are $x = 0$ and $x = -\frac{1}{4}$ .

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Question Solve the equation −4x=16x2-4 x = 16 x^{2}−4x=16x2 for xxx.

Studdy Solution

STEP 1

1. The equation −4x=16x2-4x = 16x^2−4x=16x2 is a quadratic equation in standard form.2. The solutions can be found by factoring, completing the square, or using the quadratic formula.3. The variable xxx represents a real number.

STEP 2

1. Rearrange the equation to standard quadratic form.2. Factor the quadratic expression.3. Solve for xxx by setting each factor equal to zero.

STEP 3

Rearrange the equation to standard quadratic form by moving all terms to one side of the equation.16x2+4x=0 16x^2 + 4x = 0 16x2+4x=0

STEP 4

Factor out the common factor from the quadratic expression.x(16x+4)=0 x(16x + 4) = 0 x(16x+4)=0

STEP 5

Further factor the expression by factoring out the common factor of 4 in the second term.x(4(4x+1))=0 x(4(4x + 1)) = 0 x(4(4x+1))=0

STEP 6

Set each factor equal to zero to solve for xxx.x=0and4(4x+1)=0 x = 0 \quad \text{and} \quad 4(4x + 1) = 0 x=0and4(4x+1)=0

STEP 7

Solve the second equation for xxx.4x+1=0 4x + 1 = 0 4x+1=0 4x=−1 4x = -1 4x=−1 x=−14 x = -\frac{1}{4} x=−41​

STEP 8

Combine the solutions from both factors.The solutions are x=0x = 0x=0 and x=−14x = -\frac{1}{4}x=−41​.

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Question Solve the equation $-4 x = 16 x^{2}$ for $x$ .

1. The equation $-4x = 16x^2$ is a quadratic equation in standard form.
2. The solutions can be found by factoring, completing the square, or using the quadratic formula.
3. The variable $x$ represents a real number.

1. Rearrange the equation to standard quadratic form.
2. Factor the quadratic expression.
3. Solve for $x$ by setting each factor equal to zero.

Rearrange the equation to standard quadratic form by moving all terms to one side of the equation.
$16x^2 + 4x = 0$

Factor out the common factor from the quadratic expression.
$x(16x + 4) = 0$

Further factor the expression by factoring out the common factor of 4 in the second term.
$x(4(4x + 1)) = 0$

Set each factor equal to zero to solve for $x$ .
$x = 0 \quad \text{and} \quad 4(4x + 1) = 0$

Solve the second equation for $x$ .
$4x + 1 = 0$ $4x = -1$ $x = -\frac{1}{4}$

Combine the solutions from both factors.
The solutions are $x = 0$ and $x = -\frac{1}{4}$ .