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Simplifying 59x2 + -7x + -8 = 0 Reorder the terms: -8 + -7x + 59x2 = 0 Solving -8 + -7x + 59x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 59 the coefficient of the squared term: Divide each side by '59'. -0.1355932203 + -0.1186440678x + x2 = 0 Move the constant term to the right: Add '0.1355932203' to each side of the equation. -0.1355932203 + -0.1186440678x + 0.1355932203 + x2 = 0 + 0.1355932203 Reorder the terms: -0.1355932203 + 0.1355932203 + -0.1186440678x + x2 = 0 + 0.1355932203 Combine like terms: -0.1355932203 + 0.1355932203 = 0.0000000000 0.0000000000 + -0.1186440678x + x2 = 0 + 0.1355932203 -0.1186440678x + x2 = 0 + 0.1355932203 Combine like terms: 0 + 0.1355932203 = 0.1355932203 -0.1186440678x + x2 = 0.1355932203 The x term is -0.1186440678x. Take half its coefficient (-0.0593220339). Square it (0.003519103706) and add it to both sides. Add '0.003519103706' to each side of the equation. -0.1186440678x + 0.003519103706 + x2 = 0.1355932203 + 0.003519103706 Reorder the terms: 0.003519103706 + -0.1186440678x + x2 = 0.1355932203 + 0.003519103706 Combine like terms: 0.1355932203 + 0.003519103706 = 0.139112324006 0.003519103706 + -0.1186440678x + x2 = 0.139112324006 Factor a perfect square on the left side: (x + -0.0593220339)(x + -0.0593220339) = 0.139112324006 Calculate the square root of the right side: 0.372977645 Break this problem into two subproblems by setting (x + -0.0593220339) equal to 0.372977645 and -0.372977645.Subproblem 1
x + -0.0593220339 = 0.372977645 Simplifying x + -0.0593220339 = 0.372977645 Reorder the terms: -0.0593220339 + x = 0.372977645 Solving -0.0593220339 + x = 0.372977645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0593220339' to each side of the equation. -0.0593220339 + 0.0593220339 + x = 0.372977645 + 0.0593220339 Combine like terms: -0.0593220339 + 0.0593220339 = 0.0000000000 0.0000000000 + x = 0.372977645 + 0.0593220339 x = 0.372977645 + 0.0593220339 Combine like terms: 0.372977645 + 0.0593220339 = 0.4322996789 x = 0.4322996789 Simplifying x = 0.4322996789Subproblem 2
x + -0.0593220339 = -0.372977645 Simplifying x + -0.0593220339 = -0.372977645 Reorder the terms: -0.0593220339 + x = -0.372977645 Solving -0.0593220339 + x = -0.372977645 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.0593220339' to each side of the equation. -0.0593220339 + 0.0593220339 + x = -0.372977645 + 0.0593220339 Combine like terms: -0.0593220339 + 0.0593220339 = 0.0000000000 0.0000000000 + x = -0.372977645 + 0.0593220339 x = -0.372977645 + 0.0593220339 Combine like terms: -0.372977645 + 0.0593220339 = -0.3136556111 x = -0.3136556111 Simplifying x = -0.3136556111Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4322996789, -0.3136556111}
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