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Simplifying 3x2 + 1.5x + -46 = 0 Reorder the terms: -46 + 1.5x + 3x2 = 0 Solving -46 + 1.5x + 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'. -15.33333333 + 0.5x + x2 = 0 Move the constant term to the right: Add '15.33333333' to each side of the equation. -15.33333333 + 0.5x + 15.33333333 + x2 = 0 + 15.33333333 Reorder the terms: -15.33333333 + 15.33333333 + 0.5x + x2 = 0 + 15.33333333 Combine like terms: -15.33333333 + 15.33333333 = 0.00000000 0.00000000 + 0.5x + x2 = 0 + 15.33333333 0.5x + x2 = 0 + 15.33333333 Combine like terms: 0 + 15.33333333 = 15.33333333 0.5x + x2 = 15.33333333 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 15.33333333 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 15.33333333 + 0.0625 Combine like terms: 15.33333333 + 0.0625 = 15.39583333 0.0625 + 0.5x + x2 = 15.39583333 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 15.39583333 Calculate the square root of the right side: 3.923752455 Break this problem into two subproblems by setting (x + 0.25) equal to 3.923752455 and -3.923752455.Subproblem 1
x + 0.25 = 3.923752455 Simplifying x + 0.25 = 3.923752455 Reorder the terms: 0.25 + x = 3.923752455 Solving 0.25 + x = 3.923752455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 3.923752455 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 3.923752455 + -0.25 x = 3.923752455 + -0.25 Combine like terms: 3.923752455 + -0.25 = 3.673752455 x = 3.673752455 Simplifying x = 3.673752455Subproblem 2
x + 0.25 = -3.923752455 Simplifying x + 0.25 = -3.923752455 Reorder the terms: 0.25 + x = -3.923752455 Solving 0.25 + x = -3.923752455 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -3.923752455 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -3.923752455 + -0.25 x = -3.923752455 + -0.25 Combine like terms: -3.923752455 + -0.25 = -4.173752455 x = -4.173752455 Simplifying x = -4.173752455Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.673752455, -4.173752455}
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