Math  /  Algebra

QuestionFind a value for xx if 4x2+72=6x24 x^{2}+72=6 x^{2}

Studdy Solution

STEP 1

1. The equation 4x2+72=6x2 4x^2 + 72 = 6x^2 is a quadratic equation.
2. The goal is to isolate x x and solve for its value.
3. The equation can be simplified by combining like terms.

STEP 2

1. Simplify the equation by combining like terms.
2. Isolate the variable x x .
3. Solve for x x .

STEP 3

Start by simplifying the equation. Subtract 4x2 4x^2 from both sides to combine like terms:
4x2+72=6x2 4x^2 + 72 = 6x^2 72=6x24x2 72 = 6x^2 - 4x^2

STEP 4

Simplify the right side by performing the subtraction:
72=2x2 72 = 2x^2

STEP 5

Isolate x2 x^2 by dividing both sides by 2:
722=2x22 \frac{72}{2} = \frac{2x^2}{2} 36=x2 36 = x^2

STEP 6

Solve for x x by taking the square root of both sides. Remember to consider both the positive and negative roots:
x=±36 x = \pm \sqrt{36} x=±6 x = \pm 6
The possible values for x x are:
6and6 \boxed{6} \quad \text{and} \quad \boxed{-6}

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