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Simplifying 3x2 + -10x + -75 = 0 Reorder the terms: -75 + -10x + 3x2 = 0 Solving -75 + -10x + 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'. -25 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -3.333333333x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -3.333333333x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -3.333333333x + x2 = 0 + 25 -3.333333333x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -3.333333333x + x2 = 25 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 25 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 25 + 2.777777779 Combine like terms: 25 + 2.777777779 = 27.777777779 2.777777779 + -3.333333333x + x2 = 27.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 27.777777779 Calculate the square root of the right side: 5.270462767 Break this problem into two subproblems by setting (x + -1.666666667) equal to 5.270462767 and -5.270462767.Subproblem 1
x + -1.666666667 = 5.270462767 Simplifying x + -1.666666667 = 5.270462767 Reorder the terms: -1.666666667 + x = 5.270462767 Solving -1.666666667 + x = 5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 5.270462767 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 5.270462767 + 1.666666667 x = 5.270462767 + 1.666666667 Combine like terms: 5.270462767 + 1.666666667 = 6.937129434 x = 6.937129434 Simplifying x = 6.937129434Subproblem 2
x + -1.666666667 = -5.270462767 Simplifying x + -1.666666667 = -5.270462767 Reorder the terms: -1.666666667 + x = -5.270462767 Solving -1.666666667 + x = -5.270462767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -5.270462767 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -5.270462767 + 1.666666667 x = -5.270462767 + 1.666666667 Combine like terms: -5.270462767 + 1.666666667 = -3.6037961 x = -3.6037961 Simplifying x = -3.6037961Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.937129434, -3.6037961}
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