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Simplifying x = 6x2 + -17x + 5 Reorder the terms: x = 5 + -17x + 6x2 Solving x = 5 + -17x + 6x2 Solving for variable 'x'. Reorder the terms: -5 + x + 17x + -6x2 = 5 + -17x + 6x2 + -5 + 17x + -6x2 Combine like terms: x + 17x = 18x -5 + 18x + -6x2 = 5 + -17x + 6x2 + -5 + 17x + -6x2 Reorder the terms: -5 + 18x + -6x2 = 5 + -5 + -17x + 17x + 6x2 + -6x2 Combine like terms: 5 + -5 = 0 -5 + 18x + -6x2 = 0 + -17x + 17x + 6x2 + -6x2 -5 + 18x + -6x2 = -17x + 17x + 6x2 + -6x2 Combine like terms: -17x + 17x = 0 -5 + 18x + -6x2 = 0 + 6x2 + -6x2 -5 + 18x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -5 + 18x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.8333333333 + -3x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -3x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -3x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -3x + x2 = 0 + -0.8333333333 -3x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -3x + x2 = -0.8333333333 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.8333333333 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.8333333333 + 2.25 Combine like terms: -0.8333333333 + 2.25 = 1.4166666667 2.25 + -3x + x2 = 1.4166666667 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 1.4166666667 Calculate the square root of the right side: 1.190238071 Break this problem into two subproblems by setting (x + -1.5) equal to 1.190238071 and -1.190238071.Subproblem 1
x + -1.5 = 1.190238071 Simplifying x + -1.5 = 1.190238071 Reorder the terms: -1.5 + x = 1.190238071 Solving -1.5 + x = 1.190238071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.190238071 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.190238071 + 1.5 x = 1.190238071 + 1.5 Combine like terms: 1.190238071 + 1.5 = 2.690238071 x = 2.690238071 Simplifying x = 2.690238071Subproblem 2
x + -1.5 = -1.190238071 Simplifying x + -1.5 = -1.190238071 Reorder the terms: -1.5 + x = -1.190238071 Solving -1.5 + x = -1.190238071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.190238071 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.190238071 + 1.5 x = -1.190238071 + 1.5 Combine like terms: -1.190238071 + 1.5 = 0.309761929 x = 0.309761929 Simplifying x = 0.309761929Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.690238071, 0.309761929}
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