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Simplifying 1.5x2 + 60x + -190 = 0 Reorder the terms: -190 + 60x + 1.5x2 = 0 Solving -190 + 60x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -126.6666667 + 40x + x2 = 0 Move the constant term to the right: Add '126.6666667' to each side of the equation. -126.6666667 + 40x + 126.6666667 + x2 = 0 + 126.6666667 Reorder the terms: -126.6666667 + 126.6666667 + 40x + x2 = 0 + 126.6666667 Combine like terms: -126.6666667 + 126.6666667 = 0.0000000 0.0000000 + 40x + x2 = 0 + 126.6666667 40x + x2 = 0 + 126.6666667 Combine like terms: 0 + 126.6666667 = 126.6666667 40x + x2 = 126.6666667 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 126.6666667 + 400 Reorder the terms: 400 + 40x + x2 = 126.6666667 + 400 Combine like terms: 126.6666667 + 400 = 526.6666667 400 + 40x + x2 = 526.6666667 Factor a perfect square on the left side: (x + 20)(x + 20) = 526.6666667 Calculate the square root of the right side: 22.949219305 Break this problem into two subproblems by setting (x + 20) equal to 22.949219305 and -22.949219305.Subproblem 1
x + 20 = 22.949219305 Simplifying x + 20 = 22.949219305 Reorder the terms: 20 + x = 22.949219305 Solving 20 + x = 22.949219305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 22.949219305 + -20 Combine like terms: 20 + -20 = 0 0 + x = 22.949219305 + -20 x = 22.949219305 + -20 Combine like terms: 22.949219305 + -20 = 2.949219305 x = 2.949219305 Simplifying x = 2.949219305Subproblem 2
x + 20 = -22.949219305 Simplifying x + 20 = -22.949219305 Reorder the terms: 20 + x = -22.949219305 Solving 20 + x = -22.949219305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -22.949219305 + -20 Combine like terms: 20 + -20 = 0 0 + x = -22.949219305 + -20 x = -22.949219305 + -20 Combine like terms: -22.949219305 + -20 = -42.949219305 x = -42.949219305 Simplifying x = -42.949219305Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.949219305, -42.949219305}
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