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Simplifying 3x2 + 90x + 50 = 0 Reorder the terms: 50 + 90x + 3x2 = 0 Solving 50 + 90x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 16.66666667 + 30x + x2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + 30x + -16.66666667 + x2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + 30x + x2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + 30x + x2 = 0 + -16.66666667 30x + x2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 30x + x2 = -16.66666667 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -16.66666667 + 225 Reorder the terms: 225 + 30x + x2 = -16.66666667 + 225 Combine like terms: -16.66666667 + 225 = 208.33333333 225 + 30x + x2 = 208.33333333 Factor a perfect square on the left side: (x + 15)(x + 15) = 208.33333333 Calculate the square root of the right side: 14.43375673 Break this problem into two subproblems by setting (x + 15) equal to 14.43375673 and -14.43375673.Subproblem 1
x + 15 = 14.43375673 Simplifying x + 15 = 14.43375673 Reorder the terms: 15 + x = 14.43375673 Solving 15 + x = 14.43375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 14.43375673 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.43375673 + -15 x = 14.43375673 + -15 Combine like terms: 14.43375673 + -15 = -0.56624327 x = -0.56624327 Simplifying x = -0.56624327Subproblem 2
x + 15 = -14.43375673 Simplifying x + 15 = -14.43375673 Reorder the terms: 15 + x = -14.43375673 Solving 15 + x = -14.43375673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -14.43375673 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.43375673 + -15 x = -14.43375673 + -15 Combine like terms: -14.43375673 + -15 = -29.43375673 x = -29.43375673 Simplifying x = -29.43375673Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.56624327, -29.43375673}
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