Solve 2x 7=(x 1)^2-3 - ScanMath

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Type your math problem... 2x 7=(x 1)^2-3

Question

Solve the quadratic equation

Solve using the quadratic formula

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Solve by completing the square

Solve using the PQ formula

x_{1} = 7 - 213, x_{2} = 7 + 213

Alternative Form

x_{1} \approx - 0.211103, x_{2} \approx 14.211103

Evaluate

2 x \times 7 = (x \times 1)^{2} - 3

Multiply the terms

14 x = (x \times 1)^{2} - 3

Any expression multiplied by 1 remains the same

14 x = x^{2} - 3

Swap the sides

x^{2} - 3 = 14 x

Move the expression to the left side

x^{2} - 3 - 14 x = 0

Rewrite in standard form

x^{2} - 14 x - 3 = 0

Substitute a= 1,b= - 14 and c= - 3 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{14 \pm ( - 14 ) ^{2} - 4 ( - 3 )}{2}

Simplify the expression

More Steps

x = \frac{14 \pm 208}{2}

Simplify the radical expression

More Steps

x = \frac{14 \pm 4 13}{2}

Separate the equation into 2 possible cases

x = \frac{14 + 4 13}{2} x = \frac{14 - 4 13}{2}

Simplify the expression

More Steps

x = 7 + 213 x = \frac{14 - 4 13}{2}

Simplify the expression

More Steps

x = 7 + 213 x = 7 - 213

Solution

x_{1} = 7 - 213, x_{2} = 7 + 213

Alternative Form

x_{1} \approx - 0.211103, x_{2} \approx 14.211103

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