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Simplifying 5x2 + -29x + 18 = 0 Reorder the terms: 18 + -29x + 5x2 = 0 Solving 18 + -29x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.6 + -5.8x + x2 = 0 Move the constant term to the right: Add '-3.6' to each side of the equation. 3.6 + -5.8x + -3.6 + x2 = 0 + -3.6 Reorder the terms: 3.6 + -3.6 + -5.8x + x2 = 0 + -3.6 Combine like terms: 3.6 + -3.6 = 0.0 0.0 + -5.8x + x2 = 0 + -3.6 -5.8x + x2 = 0 + -3.6 Combine like terms: 0 + -3.6 = -3.6 -5.8x + x2 = -3.6 The x term is -5.8x. Take half its coefficient (-2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. -5.8x + 8.41 + x2 = -3.6 + 8.41 Reorder the terms: 8.41 + -5.8x + x2 = -3.6 + 8.41 Combine like terms: -3.6 + 8.41 = 4.81 8.41 + -5.8x + x2 = 4.81 Factor a perfect square on the left side: (x + -2.9)(x + -2.9) = 4.81 Calculate the square root of the right side: 2.19317122 Break this problem into two subproblems by setting (x + -2.9) equal to 2.19317122 and -2.19317122.Subproblem 1
x + -2.9 = 2.19317122 Simplifying x + -2.9 = 2.19317122 Reorder the terms: -2.9 + x = 2.19317122 Solving -2.9 + x = 2.19317122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = 2.19317122 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = 2.19317122 + 2.9 x = 2.19317122 + 2.9 Combine like terms: 2.19317122 + 2.9 = 5.09317122 x = 5.09317122 Simplifying x = 5.09317122Subproblem 2
x + -2.9 = -2.19317122 Simplifying x + -2.9 = -2.19317122 Reorder the terms: -2.9 + x = -2.19317122 Solving -2.9 + x = -2.19317122 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.9' to each side of the equation. -2.9 + 2.9 + x = -2.19317122 + 2.9 Combine like terms: -2.9 + 2.9 = 0.0 0.0 + x = -2.19317122 + 2.9 x = -2.19317122 + 2.9 Combine like terms: -2.19317122 + 2.9 = 0.70682878 x = 0.70682878 Simplifying x = 0.70682878Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.09317122, 0.70682878}
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