Solve the equation by taking square roots and check the answer. 7x^2+1=-140

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The roots of `7x^2+1=-140` have to be determined.

`7x^2+1=-140`

=> `7x^2=-140-1`

=> `x^2 = -141/7`

The roots are `x1 = sqrt(141/7)*i` and `x2 = -sqrt(141/7)*i`

Substituting the roots in the original equation:

  • `7*(sqrt(141/7)*i)^2 + 1`

= `7*(-141/7) + 1`

= -141 + 1

= -140

  • `7*(-sqrt(141/7)*i)^2 + 1`

= `7*(-141/7) + 1`

= -141 + 1

= -140

This proves that the roots of the equation are ` +-sqrt(141/7)*i`

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renerlita | (Level 1) eNoter

Posted on

Step # 01: Simplify 7x

2

+1 - -140 //------------ Equation at the end of step 01 : 7x

2

+ 141 = 0 //------------ // Step # 02: Solve 7x

2

+141 = 0 //------------ # 02.01 Solve : 7x2+141 = 0 Subtract 141 from both sides of the equation: 7x2 = -141 Divide both sides of the equation by 7: x2 = -(141/7) When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get: x = ± √ -(141/7) In Math, i is called the imaginary unit. It satisfies i2 = -1 Both i and -i are the square roots of -1 Accordingly, √ -(141/7) = √ -1•(141/7) = √ -1 •√ (141/7) = i • √ (141/7) The equation has no real solutions. It has 2 imaginary, or complex solutions. x = 0.0000 + 4.4881 i x = 0.0000 - 4.4881 i //------------ // Solutions : Two solutions were found //------------ x = 0.0000 - 4.4881 i x = 0.0000 + 4.4881 i Processing ends successfully

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