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Simplifying x2 + -10 = 4x2 + -25x + -50 Reorder the terms: -10 + x2 = 4x2 + -25x + -50 Reorder the terms: -10 + x2 = -50 + -25x + 4x2 Solving -10 + x2 = -50 + -25x + 4x2 Solving for variable 'x'. Reorder the terms: -10 + 50 + 25x + x2 + -4x2 = -50 + -25x + 4x2 + 50 + 25x + -4x2 Combine like terms: -10 + 50 = 40 40 + 25x + x2 + -4x2 = -50 + -25x + 4x2 + 50 + 25x + -4x2 Combine like terms: x2 + -4x2 = -3x2 40 + 25x + -3x2 = -50 + -25x + 4x2 + 50 + 25x + -4x2 Reorder the terms: 40 + 25x + -3x2 = -50 + 50 + -25x + 25x + 4x2 + -4x2 Combine like terms: -50 + 50 = 0 40 + 25x + -3x2 = 0 + -25x + 25x + 4x2 + -4x2 40 + 25x + -3x2 = -25x + 25x + 4x2 + -4x2 Combine like terms: -25x + 25x = 0 40 + 25x + -3x2 = 0 + 4x2 + -4x2 40 + 25x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 40 + 25x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -13.33333333 + -8.333333333x + x2 = 0 Move the constant term to the right: Add '13.33333333' to each side of the equation. -13.33333333 + -8.333333333x + 13.33333333 + x2 = 0 + 13.33333333 Reorder the terms: -13.33333333 + 13.33333333 + -8.333333333x + x2 = 0 + 13.33333333 Combine like terms: -13.33333333 + 13.33333333 = 0.00000000 0.00000000 + -8.333333333x + x2 = 0 + 13.33333333 -8.333333333x + x2 = 0 + 13.33333333 Combine like terms: 0 + 13.33333333 = 13.33333333 -8.333333333x + x2 = 13.33333333 The x term is -8.333333333x. Take half its coefficient (-4.166666667). Square it (17.36111111) and add it to both sides. Add '17.36111111' to each side of the equation. -8.333333333x + 17.36111111 + x2 = 13.33333333 + 17.36111111 Reorder the terms: 17.36111111 + -8.333333333x + x2 = 13.33333333 + 17.36111111 Combine like terms: 13.33333333 + 17.36111111 = 30.69444444 17.36111111 + -8.333333333x + x2 = 30.69444444 Factor a perfect square on the left side: (x + -4.166666667)(x + -4.166666667) = 30.69444444 Calculate the square root of the right side: 5.540256712 Break this problem into two subproblems by setting (x + -4.166666667) equal to 5.540256712 and -5.540256712.Subproblem 1
x + -4.166666667 = 5.540256712 Simplifying x + -4.166666667 = 5.540256712 Reorder the terms: -4.166666667 + x = 5.540256712 Solving -4.166666667 + x = 5.540256712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 5.540256712 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 5.540256712 + 4.166666667 x = 5.540256712 + 4.166666667 Combine like terms: 5.540256712 + 4.166666667 = 9.706923379 x = 9.706923379 Simplifying x = 9.706923379Subproblem 2
x + -4.166666667 = -5.540256712 Simplifying x + -4.166666667 = -5.540256712 Reorder the terms: -4.166666667 + x = -5.540256712 Solving -4.166666667 + x = -5.540256712 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -5.540256712 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -5.540256712 + 4.166666667 x = -5.540256712 + 4.166666667 Combine like terms: -5.540256712 + 4.166666667 = -1.373590045 x = -1.373590045 Simplifying x = -1.373590045Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.706923379, -1.373590045}
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