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Simplifying 0 = 5x2 + -30x + 17 Reorder the terms: 0 = 17 + -30x + 5x2 Solving 0 = 17 + -30x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -17 = -17 -17 + 30x + -5x2 = 17 + -30x + 5x2 + -17 + 30x + -5x2 Reorder the terms: -17 + 30x + -5x2 = 17 + -17 + -30x + 30x + 5x2 + -5x2 Combine like terms: 17 + -17 = 0 -17 + 30x + -5x2 = 0 + -30x + 30x + 5x2 + -5x2 -17 + 30x + -5x2 = -30x + 30x + 5x2 + -5x2 Combine like terms: -30x + 30x = 0 -17 + 30x + -5x2 = 0 + 5x2 + -5x2 -17 + 30x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -17 + 30x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3.4 + -6x + x2 = 0 Move the constant term to the right: Add '-3.4' to each side of the equation. 3.4 + -6x + -3.4 + x2 = 0 + -3.4 Reorder the terms: 3.4 + -3.4 + -6x + x2 = 0 + -3.4 Combine like terms: 3.4 + -3.4 = 0.0 0.0 + -6x + x2 = 0 + -3.4 -6x + x2 = 0 + -3.4 Combine like terms: 0 + -3.4 = -3.4 -6x + x2 = -3.4 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -3.4 + 9 Reorder the terms: 9 + -6x + x2 = -3.4 + 9 Combine like terms: -3.4 + 9 = 5.6 9 + -6x + x2 = 5.6 Factor a perfect square on the left side: (x + -3)(x + -3) = 5.6 Calculate the square root of the right side: 2.366431913 Break this problem into two subproblems by setting (x + -3) equal to 2.366431913 and -2.366431913.Subproblem 1
x + -3 = 2.366431913 Simplifying x + -3 = 2.366431913 Reorder the terms: -3 + x = 2.366431913 Solving -3 + x = 2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.366431913 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.366431913 + 3 x = 2.366431913 + 3 Combine like terms: 2.366431913 + 3 = 5.366431913 x = 5.366431913 Simplifying x = 5.366431913Subproblem 2
x + -3 = -2.366431913 Simplifying x + -3 = -2.366431913 Reorder the terms: -3 + x = -2.366431913 Solving -3 + x = -2.366431913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.366431913 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.366431913 + 3 x = -2.366431913 + 3 Combine like terms: -2.366431913 + 3 = 0.633568087 x = 0.633568087 Simplifying x = 0.633568087Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.366431913, 0.633568087}
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