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Simplifying 17x2 + -92x + -300 = 0 Reorder the terms: -300 + -92x + 17x2 = 0 Solving -300 + -92x + 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'. -17.64705882 + -5.411764706x + x2 = 0 Move the constant term to the right: Add '17.64705882' to each side of the equation. -17.64705882 + -5.411764706x + 17.64705882 + x2 = 0 + 17.64705882 Reorder the terms: -17.64705882 + 17.64705882 + -5.411764706x + x2 = 0 + 17.64705882 Combine like terms: -17.64705882 + 17.64705882 = 0.00000000 0.00000000 + -5.411764706x + x2 = 0 + 17.64705882 -5.411764706x + x2 = 0 + 17.64705882 Combine like terms: 0 + 17.64705882 = 17.64705882 -5.411764706x + x2 = 17.64705882 The x term is -5.411764706x. Take half its coefficient (-2.705882353). Square it (7.321799308) and add it to both sides. Add '7.321799308' to each side of the equation. -5.411764706x + 7.321799308 + x2 = 17.64705882 + 7.321799308 Reorder the terms: 7.321799308 + -5.411764706x + x2 = 17.64705882 + 7.321799308 Combine like terms: 17.64705882 + 7.321799308 = 24.968858128 7.321799308 + -5.411764706x + x2 = 24.968858128 Factor a perfect square on the left side: (x + -2.705882353)(x + -2.705882353) = 24.968858128 Calculate the square root of the right side: 4.996884842 Break this problem into two subproblems by setting (x + -2.705882353) equal to 4.996884842 and -4.996884842.Subproblem 1
x + -2.705882353 = 4.996884842 Simplifying x + -2.705882353 = 4.996884842 Reorder the terms: -2.705882353 + x = 4.996884842 Solving -2.705882353 + x = 4.996884842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.705882353' to each side of the equation. -2.705882353 + 2.705882353 + x = 4.996884842 + 2.705882353 Combine like terms: -2.705882353 + 2.705882353 = 0.000000000 0.000000000 + x = 4.996884842 + 2.705882353 x = 4.996884842 + 2.705882353 Combine like terms: 4.996884842 + 2.705882353 = 7.702767195 x = 7.702767195 Simplifying x = 7.702767195Subproblem 2
x + -2.705882353 = -4.996884842 Simplifying x + -2.705882353 = -4.996884842 Reorder the terms: -2.705882353 + x = -4.996884842 Solving -2.705882353 + x = -4.996884842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.705882353' to each side of the equation. -2.705882353 + 2.705882353 + x = -4.996884842 + 2.705882353 Combine like terms: -2.705882353 + 2.705882353 = 0.000000000 0.000000000 + x = -4.996884842 + 2.705882353 x = -4.996884842 + 2.705882353 Combine like terms: -4.996884842 + 2.705882353 = -2.291002489 x = -2.291002489 Simplifying x = -2.291002489Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.702767195, -2.291002489}
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