Exercise 36 Page 159

We want to solve the quadratic equation by completing the square. To do so, we will start by rewriting the equation so all terms with x are on one side of the equation and the constant term is on the other side. -3x^2+4=0 ⇓ -3x^2=-4 Now, let's divide each side by -3 so that the coefficient of x^2 will be 1.

-3x^2=-4

DivEqn

.LHS /(-3).=.RHS /(-3).

-3x^2/-3=-4/-3

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Simplify

DivNegNeg

- a/- b=a/b

3x^2/3=4/3

MovePartNumRight

a* b/c=a/c* b

3/3x^2=4/3

QuotOne

a/a=1

1x^2=4/3

IdPropMult

Identity Property of Multiplication

x^2=4/3

In a quadratic expression, b is the linear coefficient. From the equation above, we know that b=0. Let's now calculate ( b2 )^2.

( b/2 )^2

Substitute

b= 0

( 0/2 )^2

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Simplify

0/a=0

0^2

CalcPow

Calculate power

0

Since ( b2 )^2=0, we do not need to add anything to our equation.

x^2=4/3

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=± sqrt(4/3)

SqrtQuot

sqrt(a/b)=sqrt(a)/sqrt(b)

x=± sqrt(4)/sqrt(3)

CalcRoot

Calculate root

x=±2/sqrt(3)

UseCalc

Use a calculator

x=± 1.154700 ...

RoundDec

Round to 1 decimal place(s)

x≈ ± 1.2

Both x≈ 1.2 and x≈ - 1.2 are solutions to the equation, to the nearest tenth.