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Simplifying 3x2 + 10x = 120 Reorder the terms: 10x + 3x2 = 120 Solving 10x + 3x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 10x + 3x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -40 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 3.333333333x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 3.333333333x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 3.333333333x + x2 = 0 + 40 3.333333333x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 3.333333333x + x2 = 40 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 40 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 40 + 2.777777779 Combine like terms: 40 + 2.777777779 = 42.777777779 2.777777779 + 3.333333333x + x2 = 42.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 42.777777779 Calculate the square root of the right side: 6.54047229 Break this problem into two subproblems by setting (x + 1.666666667) equal to 6.54047229 and -6.54047229.Subproblem 1
x + 1.666666667 = 6.54047229 Simplifying x + 1.666666667 = 6.54047229 Reorder the terms: 1.666666667 + x = 6.54047229 Solving 1.666666667 + x = 6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 6.54047229 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 6.54047229 + -1.666666667 x = 6.54047229 + -1.666666667 Combine like terms: 6.54047229 + -1.666666667 = 4.873805623 x = 4.873805623 Simplifying x = 4.873805623Subproblem 2
x + 1.666666667 = -6.54047229 Simplifying x + 1.666666667 = -6.54047229 Reorder the terms: 1.666666667 + x = -6.54047229 Solving 1.666666667 + x = -6.54047229 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -6.54047229 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -6.54047229 + -1.666666667 x = -6.54047229 + -1.666666667 Combine like terms: -6.54047229 + -1.666666667 = -8.207138957 x = -8.207138957 Simplifying x = -8.207138957Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.873805623, -8.207138957}
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