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Simplifying 3x2 + 190x + -300 = 0 Reorder the terms: -300 + 190x + 3x2 = 0 Solving -300 + 190x + 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'. -100 + 63.33333333x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 63.33333333x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 63.33333333x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 63.33333333x + x2 = 0 + 100 63.33333333x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 63.33333333x + x2 = 100 The x term is 63.33333333x. Take half its coefficient (31.66666667). Square it (1002.777778) and add it to both sides. Add '1002.777778' to each side of the equation. 63.33333333x + 1002.777778 + x2 = 100 + 1002.777778 Reorder the terms: 1002.777778 + 63.33333333x + x2 = 100 + 1002.777778 Combine like terms: 100 + 1002.777778 = 1102.777778 1002.777778 + 63.33333333x + x2 = 1102.777778 Factor a perfect square on the left side: (x + 31.66666667)(x + 31.66666667) = 1102.777778 Calculate the square root of the right side: 33.208098079 Break this problem into two subproblems by setting (x + 31.66666667) equal to 33.208098079 and -33.208098079.Subproblem 1
x + 31.66666667 = 33.208098079 Simplifying x + 31.66666667 = 33.208098079 Reorder the terms: 31.66666667 + x = 33.208098079 Solving 31.66666667 + x = 33.208098079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.66666667' to each side of the equation. 31.66666667 + -31.66666667 + x = 33.208098079 + -31.66666667 Combine like terms: 31.66666667 + -31.66666667 = 0.00000000 0.00000000 + x = 33.208098079 + -31.66666667 x = 33.208098079 + -31.66666667 Combine like terms: 33.208098079 + -31.66666667 = 1.541431409 x = 1.541431409 Simplifying x = 1.541431409Subproblem 2
x + 31.66666667 = -33.208098079 Simplifying x + 31.66666667 = -33.208098079 Reorder the terms: 31.66666667 + x = -33.208098079 Solving 31.66666667 + x = -33.208098079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.66666667' to each side of the equation. 31.66666667 + -31.66666667 + x = -33.208098079 + -31.66666667 Combine like terms: 31.66666667 + -31.66666667 = 0.00000000 0.00000000 + x = -33.208098079 + -31.66666667 x = -33.208098079 + -31.66666667 Combine like terms: -33.208098079 + -31.66666667 = -64.874764749 x = -64.874764749 Simplifying x = -64.874764749Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.541431409, -64.874764749}
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