Try it 4 Transform each quadratic equation to standard form. Write the equation with a positive coefficient for the second-degree term. Solve and check. 2. x(x +11) = 2(x+5) b. 3x = SR 10x2-5x-24 SR-Square Root Paki Ayos po ng sagot Pakiusap lang po Thank you❤️. Created by sssofiaangelaaa07. Math

Try it 4 Transform each quadratic equation to standard form. Write the equation ...

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Transforming a Quadratic Equation to a Standard Form

The standard form of:

a) $x(x + 11) = 2(x + 5)$

b) $3x = \sqrt{10x^2 - 5x - 24}$

$\mathbb{\bold{\magenta{STEP-BY-STEP \: SOLUTION:}}}$

a) $x(x + 11) = 2(x + 5)$

To transform:

» Apply the Distributive Property to simplify the two expressions.

$x^2 + 11x = 2x + 10$

» Zero-out terms from the right-side expression to left-side by APE (Addition Property of Equality).

$x^2 + 11x - 2x - 10 = 0$

» Combine like terms.

$x^2 + 9x - 10 = 0$

» Solve by factoring.

$(x - 1)(x + 10) = 0$

» Apply the Zero-Product Property.

$x_1 = 1 ; x_2 = -10$

Check: $x(x + 11) = 2(x + 5) ; x = 1, -10$

$\boxed{\begin{array}{c} x(x + 11) = 2(x + 5) ; x = 1\\1(1 + 11) = 2(1 + 5)\\1 + 11 = 2 + 10\\12 = 12 \: ; \rm (TRUE)\end{array}} \ \ \boxed{\begin{array}{c} x(x + 11) = 2(x + 5) ; x = -10\\ -10(-10 + 11) = 2(-10 + 5)\\ 100 + (-110) = -20 + 10\\-10 = -10 \: ; \rm (TRUE)\end{array}}$

b) $3x = \sqrt{10x^2 - 5x - 24}$

To transform:

» Square both sides.

$(3x)^2 = (\sqrt{10x^2 - 5x - 24})^2$

» Simplify.

$9x = \sqrt{10x^2 - 5x - 24}$

» Solve by APE (Addition Property of Equality).

$9x - 10x^2 + 5x + 24 = 0$

» Combine like terms.

$-x^2 + 5x + 24 = 0$

» Write the equation with a positive coefficient for the second-degree term.

$x^2 - 5x - 24 = 0$

» Solve by factoring.

$(x-8)(x+3)$

» Apply the Zero-Product Property.

$x_1 = 8 ; x_2 = -3$

Check: $3x = \sqrt{10x^2 - 5x - 24}; x = 8, -3$

$\boxed{\begin{array}{c} 3x = \sqrt{10x^2 - 5x - 24} \: ; x = 8\\3(8) = \sqrt{10(8)^2 - 5(8) - 24}\\ 24 = \sqrt{10(64)- 40 - 24}\\24 = \sqrt{640-40-24} \\ 24 = \sqrt{600 - 24}\\ 24 = \sqrt{576}\\ 24 = 24 \: ; \rm (TRUE)\end{array}} \ \ \boxed{\begin{array}{c} 3x = \sqrt{10x^2 - 5x - 24} \: ; x = -3\\3(-3) = \sqrt{10(-3)^2 - 5(-3) - 24}\\ -9 = \sqrt{10(9) + 15 - 24}\\ -9 = \sqrt{90 + 15 - 24} \\ -9 = \sqrt{105 - 24}\\ -9 = \sqrt{81}\\ -9 = -9 \: ; \rm (TRUE)\end{array}}$

$\mathbb{\bold{\orange{FINAL \: ANSWER:}}}$

a) $x(x + 11) = 2(x + 5) \Rightarrow \boxed{x^2 + 9x - 10 = 0}$

b) $3x = \sqrt{10x^2 - 5x - 24} \Rightarrow \boxed{x^2 - 5x - 24 = 0}$

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