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Simplifying 3x2 + -15x + -23 = 0 Reorder the terms: -23 + -15x + 3x2 = 0 Solving -23 + -15x + 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'. -7.666666667 + -5x + x2 = 0 Move the constant term to the right: Add '7.666666667' to each side of the equation. -7.666666667 + -5x + 7.666666667 + x2 = 0 + 7.666666667 Reorder the terms: -7.666666667 + 7.666666667 + -5x + x2 = 0 + 7.666666667 Combine like terms: -7.666666667 + 7.666666667 = 0.000000000 0.000000000 + -5x + x2 = 0 + 7.666666667 -5x + x2 = 0 + 7.666666667 Combine like terms: 0 + 7.666666667 = 7.666666667 -5x + x2 = 7.666666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 7.666666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 7.666666667 + 6.25 Combine like terms: 7.666666667 + 6.25 = 13.916666667 6.25 + -5x + x2 = 13.916666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 13.916666667 Calculate the square root of the right side: 3.730504881 Break this problem into two subproblems by setting (x + -2.5) equal to 3.730504881 and -3.730504881.Subproblem 1
x + -2.5 = 3.730504881 Simplifying x + -2.5 = 3.730504881 Reorder the terms: -2.5 + x = 3.730504881 Solving -2.5 + x = 3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.730504881 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.730504881 + 2.5 x = 3.730504881 + 2.5 Combine like terms: 3.730504881 + 2.5 = 6.230504881 x = 6.230504881 Simplifying x = 6.230504881Subproblem 2
x + -2.5 = -3.730504881 Simplifying x + -2.5 = -3.730504881 Reorder the terms: -2.5 + x = -3.730504881 Solving -2.5 + x = -3.730504881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.730504881 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.730504881 + 2.5 x = -3.730504881 + 2.5 Combine like terms: -3.730504881 + 2.5 = -1.230504881 x = -1.230504881 Simplifying x = -1.230504881Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.230504881, -1.230504881}
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