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Simplifying 3x2 + 22x + 40 = 100 Reorder the terms: 40 + 22x + 3x2 = 100 Solving 40 + 22x + 3x2 = 100 Solving for variable 'x'. Reorder the terms: 40 + -100 + 22x + 3x2 = 100 + -100 Combine like terms: 40 + -100 = -60 -60 + 22x + 3x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -60 + 22x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -20 + 7.333333333x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 7.333333333x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + 7.333333333x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 7.333333333x + x2 = 0 + 20 7.333333333x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 7.333333333x + x2 = 20 The x term is 7.333333333x. Take half its coefficient (3.666666667). Square it (13.44444445) and add it to both sides. Add '13.44444445' to each side of the equation. 7.333333333x + 13.44444445 + x2 = 20 + 13.44444445 Reorder the terms: 13.44444445 + 7.333333333x + x2 = 20 + 13.44444445 Combine like terms: 20 + 13.44444445 = 33.44444445 13.44444445 + 7.333333333x + x2 = 33.44444445 Factor a perfect square on the left side: (x + 3.666666667)(x + 3.666666667) = 33.44444445 Calculate the square root of the right side: 5.783117191 Break this problem into two subproblems by setting (x + 3.666666667) equal to 5.783117191 and -5.783117191.Subproblem 1
x + 3.666666667 = 5.783117191 Simplifying x + 3.666666667 = 5.783117191 Reorder the terms: 3.666666667 + x = 5.783117191 Solving 3.666666667 + x = 5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = 5.783117191 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = 5.783117191 + -3.666666667 x = 5.783117191 + -3.666666667 Combine like terms: 5.783117191 + -3.666666667 = 2.116450524 x = 2.116450524 Simplifying x = 2.116450524Subproblem 2
x + 3.666666667 = -5.783117191 Simplifying x + 3.666666667 = -5.783117191 Reorder the terms: 3.666666667 + x = -5.783117191 Solving 3.666666667 + x = -5.783117191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.666666667' to each side of the equation. 3.666666667 + -3.666666667 + x = -5.783117191 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + x = -5.783117191 + -3.666666667 x = -5.783117191 + -3.666666667 Combine like terms: -5.783117191 + -3.666666667 = -9.449783858 x = -9.449783858 Simplifying x = -9.449783858Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.116450524, -9.449783858}
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