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Simplifying 0.112x2 + 0.2399x + -0.2603 = 0 Reorder the terms: -0.2603 + 0.2399x + 0.112x2 = 0 Solving -0.2603 + 0.2399x + 0.112x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.112 the coefficient of the squared term: Divide each side by '0.112'. -2.324107143 + 2.141964286x + x2 = 0 Move the constant term to the right: Add '2.324107143' to each side of the equation. -2.324107143 + 2.141964286x + 2.324107143 + x2 = 0 + 2.324107143 Reorder the terms: -2.324107143 + 2.324107143 + 2.141964286x + x2 = 0 + 2.324107143 Combine like terms: -2.324107143 + 2.324107143 = 0.000000000 0.000000000 + 2.141964286x + x2 = 0 + 2.324107143 2.141964286x + x2 = 0 + 2.324107143 Combine like terms: 0 + 2.324107143 = 2.324107143 2.141964286x + x2 = 2.324107143 The x term is 2.141964286x. Take half its coefficient (1.070982143). Square it (1.147002751) and add it to both sides. Add '1.147002751' to each side of the equation. 2.141964286x + 1.147002751 + x2 = 2.324107143 + 1.147002751 Reorder the terms: 1.147002751 + 2.141964286x + x2 = 2.324107143 + 1.147002751 Combine like terms: 2.324107143 + 1.147002751 = 3.471109894 1.147002751 + 2.141964286x + x2 = 3.471109894 Factor a perfect square on the left side: (x + 1.070982143)(x + 1.070982143) = 3.471109894 Calculate the square root of the right side: 1.863091488 Break this problem into two subproblems by setting (x + 1.070982143) equal to 1.863091488 and -1.863091488.Subproblem 1
x + 1.070982143 = 1.863091488 Simplifying x + 1.070982143 = 1.863091488 Reorder the terms: 1.070982143 + x = 1.863091488 Solving 1.070982143 + x = 1.863091488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.070982143' to each side of the equation. 1.070982143 + -1.070982143 + x = 1.863091488 + -1.070982143 Combine like terms: 1.070982143 + -1.070982143 = 0.000000000 0.000000000 + x = 1.863091488 + -1.070982143 x = 1.863091488 + -1.070982143 Combine like terms: 1.863091488 + -1.070982143 = 0.792109345 x = 0.792109345 Simplifying x = 0.792109345Subproblem 2
x + 1.070982143 = -1.863091488 Simplifying x + 1.070982143 = -1.863091488 Reorder the terms: 1.070982143 + x = -1.863091488 Solving 1.070982143 + x = -1.863091488 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.070982143' to each side of the equation. 1.070982143 + -1.070982143 + x = -1.863091488 + -1.070982143 Combine like terms: 1.070982143 + -1.070982143 = 0.000000000 0.000000000 + x = -1.863091488 + -1.070982143 x = -1.863091488 + -1.070982143 Combine like terms: -1.863091488 + -1.070982143 = -2.934073631 x = -2.934073631 Simplifying x = -2.934073631Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.792109345, -2.934073631}
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