anonymous
  • anonymous
Solve. x2 - 10x = -21
Mathematics
katieb
  • katieb
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mathstudent55
  • mathstudent55
First, add 21 to both sides. Once you have all three terms on left side equaling zero on right side, try to factor the left side. Then set each factor equal to zero and solve both equations. If you can't factor it, the use the quadratic formula.
anonymous
  • anonymous
Simplifying x2 + -10x = -21 Reorder the terms: -10x + x2 = -21 Solving -10x + x2 = -21 Solving for variable 'x'. Reorder the terms: 21 + -10x + x2 = -21 + 21 Combine like terms: -21 + 21 = 0 21 + -10x + x2 = 0 Factor a trinomial. (3 + -1x)(7 + -1x) = 0 Subproblem 1Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3 Subproblem 2Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solutionx = {3, 7}
anonymous
  • anonymous
oh wow thank you!

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anonymous
  • anonymous
Np :)
mathstudent55
  • mathstudent55
x^2 - 10x = -21 Add 21 to both sides: x^2 - 10x + 21 = 0 Factor left side: (x - 7)(x - 3) = 0 Set each factor equal to zero and solve: x - 7 = 0 or x - 3 = 0 x = 7 or x = 3

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