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Simplifying 34x2 + -27x + -10 = 0 Reorder the terms: -10 + -27x + 34x2 = 0 Solving -10 + -27x + 34x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.2941176471 + -0.7941176471x + x2 = 0 Move the constant term to the right: Add '0.2941176471' to each side of the equation. -0.2941176471 + -0.7941176471x + 0.2941176471 + x2 = 0 + 0.2941176471 Reorder the terms: -0.2941176471 + 0.2941176471 + -0.7941176471x + x2 = 0 + 0.2941176471 Combine like terms: -0.2941176471 + 0.2941176471 = 0.0000000000 0.0000000000 + -0.7941176471x + x2 = 0 + 0.2941176471 -0.7941176471x + x2 = 0 + 0.2941176471 Combine like terms: 0 + 0.2941176471 = 0.2941176471 -0.7941176471x + x2 = 0.2941176471 The x term is -0.7941176471x. Take half its coefficient (-0.3970588236). Square it (0.1576557094) and add it to both sides. Add '0.1576557094' to each side of the equation. -0.7941176471x + 0.1576557094 + x2 = 0.2941176471 + 0.1576557094 Reorder the terms: 0.1576557094 + -0.7941176471x + x2 = 0.2941176471 + 0.1576557094 Combine like terms: 0.2941176471 + 0.1576557094 = 0.4517733565 0.1576557094 + -0.7941176471x + x2 = 0.4517733565 Factor a perfect square on the left side: (x + -0.3970588236)(x + -0.3970588236) = 0.4517733565 Calculate the square root of the right side: 0.672140875 Break this problem into two subproblems by setting (x + -0.3970588236) equal to 0.672140875 and -0.672140875.Subproblem 1
x + -0.3970588236 = 0.672140875 Simplifying x + -0.3970588236 = 0.672140875 Reorder the terms: -0.3970588236 + x = 0.672140875 Solving -0.3970588236 + x = 0.672140875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3970588236' to each side of the equation. -0.3970588236 + 0.3970588236 + x = 0.672140875 + 0.3970588236 Combine like terms: -0.3970588236 + 0.3970588236 = 0.0000000000 0.0000000000 + x = 0.672140875 + 0.3970588236 x = 0.672140875 + 0.3970588236 Combine like terms: 0.672140875 + 0.3970588236 = 1.0691996986 x = 1.0691996986 Simplifying x = 1.0691996986Subproblem 2
x + -0.3970588236 = -0.672140875 Simplifying x + -0.3970588236 = -0.672140875 Reorder the terms: -0.3970588236 + x = -0.672140875 Solving -0.3970588236 + x = -0.672140875 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3970588236' to each side of the equation. -0.3970588236 + 0.3970588236 + x = -0.672140875 + 0.3970588236 Combine like terms: -0.3970588236 + 0.3970588236 = 0.0000000000 0.0000000000 + x = -0.672140875 + 0.3970588236 x = -0.672140875 + 0.3970588236 Combine like terms: -0.672140875 + 0.3970588236 = -0.2750820514 x = -0.2750820514 Simplifying x = -0.2750820514Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0691996986, -0.2750820514}
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