What are the solutions of the quadratic equation 49x2 9

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Gauthmathier9061

Grade 9 · 2021-10-16

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What are the solutions of the quadratic equation What are the solutions of the quadratic equation 4 - Gauthmath ?
x=\frac {1}{9} and x=-\frac {1}{9}
x=\frac {3}{7} and x=-\frac {3}{7}
x=\frac {3}{4} and x=-\frac {3}{4}
x=\frac {9}{49} and x=-\frac {9}{49}

Gauthmathier0027

Grade 9 · 2021-10-16

Answer

x = \dfrac{3}{7} or x = - \dfrac{3}{7}

Explanation

Divide both sides of the equation by the coefficient of variable: x^{2} = 9 \div 49
Rewrite as fraction: x^{2} = \dfrac{9}{49}
Split into two equations: x = \sqrt{\dfrac{9}{49}} or x = - \sqrt{\dfrac{9}{49}}
Rewrite the expression using \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}: x = \dfrac{\sqrt{9}}{\sqrt{49}}
Factor and rewrite the radicand in exponential form: x = \dfrac{\sqrt{3^{2}}}{\sqrt{7^{2}}}
Simplify the radical expression: x = \dfrac{3}{7}
Rewrite the expression using \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}: x = - \dfrac{\sqrt{9}}{\sqrt{49}}
Factor and rewrite the radicand in exponential form: x = - \dfrac{\sqrt{3^{2}}}{\sqrt{7^{2}}}
Simplify the radical expression: x = - \dfrac{3}{7}
Combine the results: x = \dfrac{3}{7} or x = - \dfrac{3}{7}
Answer: x = \dfrac{3}{7} or x = - \dfrac{3}{7}

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x=\frac{\sqrt{A+9}}{7}

x=-\frac{\sqrt{A+9}}{7}\text{, }A\geq -9

Similar Problems from Web Search

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49x^{2}-9=A

Swap sides so that all variable terms are on the left hand side.

49x^{2}=A+9

Add 9 to both sides.

\frac{49x^{2}}{49}=\frac{A+9}{49}

Divide both sides by 49.

x^{2}=\frac{A+9}{49}

Dividing by 49 undoes the multiplication by 49.

x=\frac{\sqrt{A+9}}{7} x=-\frac{\sqrt{A+9}}{7}

Take the square root of both sides of the equation.

49x^{2}-9=A

Swap sides so that all variable terms are on the left hand side.

49x^{2}-9-A=0

Subtract A from both sides.

49x^{2}-A-9=0

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

x=\frac{0±\sqrt{0^{2}-4\times 49\left(-A-9\right)}}{2\times 49}

This equation is in standard form: ax^{2}+bx+c=0. Substitute 49 for a, 0 for b, and -9-A for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

x=\frac{0±\sqrt{-4\times 49\left(-A-9\right)}}{2\times 49}

Square 0.

x=\frac{0±\sqrt{-196\left(-A-9\right)}}{2\times 49}

Multiply -4 times 49.

x=\frac{0±\sqrt{196A+1764}}{2\times 49}

Multiply -196 times -9-A.

x=\frac{0±14\sqrt{A+9}}{2\times 49}

Take the square root of 1764+196A.

x=\frac{0±14\sqrt{A+9}}{98}

Multiply 2 times 49.

x=\frac{\sqrt{A+9}}{7}

Now solve the equation x=\frac{0±14\sqrt{A+9}}{98} when ± is plus.

x=-\frac{\sqrt{A+9}}{7}

Now solve the equation x=\frac{0±14\sqrt{A+9}}{98} when ± is minus.

x=\frac{\sqrt{A+9}}{7} x=-\frac{\sqrt{A+9}}{7}

The equation is now solved.

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• Mean

• Mode

• Greatest Common Factor

• Least Common Multiple

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• Mixed Fractions

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• Combine Like Terms

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\left(7x-3\right)\left(7x+3\right)

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49 x ^ { 2 } - 9

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\left(7x-3\right)\left(7x+3\right)

Rewrite 49x^{2}-9 as \left(7x\right)^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

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