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Simplifying 3x2 = 144 + x Solving 3x2 = 144 + x Solving for variable 'x'. Reorder the terms: -144 + -1x + 3x2 = 144 + x + -144 + -1x Reorder the terms: -144 + -1x + 3x2 = 144 + -144 + x + -1x Combine like terms: 144 + -144 = 0 -144 + -1x + 3x2 = 0 + x + -1x -144 + -1x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -144 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -48 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -0.3333333333x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -0.3333333333x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -0.3333333333x + x2 = 0 + 48 -0.3333333333x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -0.3333333333x + x2 = 48 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 48 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 48 + 0.02777777779 Combine like terms: 48 + 0.02777777779 = 48.02777777779 0.02777777779 + -0.3333333333x + x2 = 48.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 48.02777777779 Calculate the square root of the right side: 6.930207629 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 6.930207629 and -6.930207629.Subproblem 1
x + -0.1666666667 = 6.930207629 Simplifying x + -0.1666666667 = 6.930207629 Reorder the terms: -0.1666666667 + x = 6.930207629 Solving -0.1666666667 + x = 6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 6.930207629 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 6.930207629 + 0.1666666667 x = 6.930207629 + 0.1666666667 Combine like terms: 6.930207629 + 0.1666666667 = 7.0968742957 x = 7.0968742957 Simplifying x = 7.0968742957Subproblem 2
x + -0.1666666667 = -6.930207629 Simplifying x + -0.1666666667 = -6.930207629 Reorder the terms: -0.1666666667 + x = -6.930207629 Solving -0.1666666667 + x = -6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -6.930207629 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -6.930207629 + 0.1666666667 x = -6.930207629 + 0.1666666667 Combine like terms: -6.930207629 + 0.1666666667 = -6.7635409623 x = -6.7635409623 Simplifying x = -6.7635409623Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.0968742957, -6.7635409623}
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