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Question Solve for xx in the equation 10=1.35x10=1.35 \sqrt{x}.

Studdy Solution

STEP 1

1. The equation 10=1.35x10 = 1.35 \sqrt{x} can be solved for the variable xx using algebraic manipulations.
2. The variable xx is a real number and x≥0x \geq 0 since it's under a square root.
3. The operations used to isolate xx will include squaring both sides of the equation to remove the square root.

STEP 2

1. Isolate the square root term.
2. Square both sides of the equation to eliminate the square root.
3. Solve for xx.

STEP 3

Divide both sides of the equation by 1.351.35 to isolate the square root term.
101.35=x \frac{10}{1.35} = \sqrt{x}

STEP 4

Calculate the division on the left-hand side to get a numerical value.
101.35≈7.4074=x \frac{10}{1.35} \approx 7.4074 = \sqrt{x}

STEP 5

Square both sides of the equation to eliminate the square root.
(7.4074)2=(x)2 (7.4074)^2 = (\sqrt{x})^2

STEP 6

Calculate the square of 7.40747.4074 and simplify the right-hand side.
54.8699≈x 54.8699 \approx x

STEP 7

State the solution for xx.
x≈54.8699 x \approx 54.8699
The solution to the equation 10=1.35x10 = 1.35 \sqrt{x} is x≈54.8699x \approx 54.8699.

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