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Simplifying 6x2 + -30x + 29 = 0 Reorder the terms: 29 + -30x + 6x2 = 0 Solving 29 + -30x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 4.833333333 + -5x + x2 = 0 Move the constant term to the right: Add '-4.833333333' to each side of the equation. 4.833333333 + -5x + -4.833333333 + x2 = 0 + -4.833333333 Reorder the terms: 4.833333333 + -4.833333333 + -5x + x2 = 0 + -4.833333333 Combine like terms: 4.833333333 + -4.833333333 = 0.000000000 0.000000000 + -5x + x2 = 0 + -4.833333333 -5x + x2 = 0 + -4.833333333 Combine like terms: 0 + -4.833333333 = -4.833333333 -5x + x2 = -4.833333333 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 = -4.833333333 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.833333333 + 6.25 Combine like terms: -4.833333333 + 6.25 = 1.416666667 6.25 + -5x + x2 = 1.416666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 1.416666667 Calculate the square root of the right side: 1.190238072 Break this problem into two subproblems by setting (x + -2.5) equal to 1.190238072 and -1.190238072.Subproblem 1
x + -2.5 = 1.190238072 Simplifying x + -2.5 = 1.190238072 Reorder the terms: -2.5 + x = 1.190238072 Solving -2.5 + x = 1.190238072 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 = 1.190238072 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.190238072 + 2.5 x = 1.190238072 + 2.5 Combine like terms: 1.190238072 + 2.5 = 3.690238072 x = 3.690238072 Simplifying x = 3.690238072Subproblem 2
x + -2.5 = -1.190238072 Simplifying x + -2.5 = -1.190238072 Reorder the terms: -2.5 + x = -1.190238072 Solving -2.5 + x = -1.190238072 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 = -1.190238072 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.190238072 + 2.5 x = -1.190238072 + 2.5 Combine like terms: -1.190238072 + 2.5 = 1.309761928 x = 1.309761928 Simplifying x = 1.309761928Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.690238072, 1.309761928}
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