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Simplifying 1 + 6x(6 + -4x) + -6x = 0 1 + (6 * 6x + -4x * 6x) + -6x = 0 1 + (36x + -24x2) + -6x = 0 Reorder the terms: 1 + 36x + -6x + -24x2 = 0 Combine like terms: 36x + -6x = 30x 1 + 30x + -24x2 = 0 Solving 1 + 30x + -24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -0.04166666667 + -1.25x + x2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -1.25x + 0.04166666667 + x2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -1.25x + x2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -1.25x + x2 = 0 + 0.04166666667 -1.25x + x2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -1.25x + x2 = 0.04166666667 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = 0.04166666667 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = 0.04166666667 + 0.390625 Combine like terms: 0.04166666667 + 0.390625 = 0.43229166667 0.390625 + -1.25x + x2 = 0.43229166667 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.43229166667 Calculate the square root of the right side: 0.65748891 Break this problem into two subproblems by setting (x + -0.625) equal to 0.65748891 and -0.65748891.Subproblem 1
x + -0.625 = 0.65748891 Simplifying x + -0.625 = 0.65748891 Reorder the terms: -0.625 + x = 0.65748891 Solving -0.625 + x = 0.65748891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.65748891 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.65748891 + 0.625 x = 0.65748891 + 0.625 Combine like terms: 0.65748891 + 0.625 = 1.28248891 x = 1.28248891 Simplifying x = 1.28248891Subproblem 2
x + -0.625 = -0.65748891 Simplifying x + -0.625 = -0.65748891 Reorder the terms: -0.625 + x = -0.65748891 Solving -0.625 + x = -0.65748891 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.65748891 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.65748891 + 0.625 x = -0.65748891 + 0.625 Combine like terms: -0.65748891 + 0.625 = -0.03248891 x = -0.03248891 Simplifying x = -0.03248891Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.28248891, -0.03248891}
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