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Simplifying 17x2 + -12x + -64 = 0 Reorder the terms: -64 + -12x + 17x2 = 0 Solving -64 + -12x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -3.764705882 + -0.7058823529x + x2 = 0 Move the constant term to the right: Add '3.764705882' to each side of the equation. -3.764705882 + -0.7058823529x + 3.764705882 + x2 = 0 + 3.764705882 Reorder the terms: -3.764705882 + 3.764705882 + -0.7058823529x + x2 = 0 + 3.764705882 Combine like terms: -3.764705882 + 3.764705882 = 0.000000000 0.000000000 + -0.7058823529x + x2 = 0 + 3.764705882 -0.7058823529x + x2 = 0 + 3.764705882 Combine like terms: 0 + 3.764705882 = 3.764705882 -0.7058823529x + x2 = 3.764705882 The x term is -0.7058823529x. Take half its coefficient (-0.3529411765). Square it (0.1245674741) and add it to both sides. Add '0.1245674741' to each side of the equation. -0.7058823529x + 0.1245674741 + x2 = 3.764705882 + 0.1245674741 Reorder the terms: 0.1245674741 + -0.7058823529x + x2 = 3.764705882 + 0.1245674741 Combine like terms: 3.764705882 + 0.1245674741 = 3.8892733561 0.1245674741 + -0.7058823529x + x2 = 3.8892733561 Factor a perfect square on the left side: (x + -0.3529411765)(x + -0.3529411765) = 3.8892733561 Calculate the square root of the right side: 1.972124072 Break this problem into two subproblems by setting (x + -0.3529411765) equal to 1.972124072 and -1.972124072.Subproblem 1
x + -0.3529411765 = 1.972124072 Simplifying x + -0.3529411765 = 1.972124072 Reorder the terms: -0.3529411765 + x = 1.972124072 Solving -0.3529411765 + x = 1.972124072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3529411765' to each side of the equation. -0.3529411765 + 0.3529411765 + x = 1.972124072 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + x = 1.972124072 + 0.3529411765 x = 1.972124072 + 0.3529411765 Combine like terms: 1.972124072 + 0.3529411765 = 2.3250652485 x = 2.3250652485 Simplifying x = 2.3250652485Subproblem 2
x + -0.3529411765 = -1.972124072 Simplifying x + -0.3529411765 = -1.972124072 Reorder the terms: -0.3529411765 + x = -1.972124072 Solving -0.3529411765 + x = -1.972124072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3529411765' to each side of the equation. -0.3529411765 + 0.3529411765 + x = -1.972124072 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + x = -1.972124072 + 0.3529411765 x = -1.972124072 + 0.3529411765 Combine like terms: -1.972124072 + 0.3529411765 = -1.6191828955 x = -1.6191828955 Simplifying x = -1.6191828955Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3250652485, -1.6191828955}
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