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Simplifying 0.16x2 + 104x + 56 = 0 Reorder the terms: 56 + 104x + 0.16x2 = 0 Solving 56 + 104x + 0.16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.16 the coefficient of the squared term: Divide each side by '0.16'. 350 + 650x + x2 = 0 Move the constant term to the right: Add '-350' to each side of the equation. 350 + 650x + -350 + x2 = 0 + -350 Reorder the terms: 350 + -350 + 650x + x2 = 0 + -350 Combine like terms: 350 + -350 = 0 0 + 650x + x2 = 0 + -350 650x + x2 = 0 + -350 Combine like terms: 0 + -350 = -350 650x + x2 = -350 The x term is 650x. Take half its coefficient (325). Square it (105625) and add it to both sides. Add '105625' to each side of the equation. 650x + 105625 + x2 = -350 + 105625 Reorder the terms: 105625 + 650x + x2 = -350 + 105625 Combine like terms: -350 + 105625 = 105275 105625 + 650x + x2 = 105275 Factor a perfect square on the left side: (x + 325)(x + 325) = 105275 Calculate the square root of the right side: 324.461091658 Break this problem into two subproblems by setting (x + 325) equal to 324.461091658 and -324.461091658.Subproblem 1
x + 325 = 324.461091658 Simplifying x + 325 = 324.461091658 Reorder the terms: 325 + x = 324.461091658 Solving 325 + x = 324.461091658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-325' to each side of the equation. 325 + -325 + x = 324.461091658 + -325 Combine like terms: 325 + -325 = 0 0 + x = 324.461091658 + -325 x = 324.461091658 + -325 Combine like terms: 324.461091658 + -325 = -0.538908342 x = -0.538908342 Simplifying x = -0.538908342Subproblem 2
x + 325 = -324.461091658 Simplifying x + 325 = -324.461091658 Reorder the terms: 325 + x = -324.461091658 Solving 325 + x = -324.461091658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-325' to each side of the equation. 325 + -325 + x = -324.461091658 + -325 Combine like terms: 325 + -325 = 0 0 + x = -324.461091658 + -325 x = -324.461091658 + -325 Combine like terms: -324.461091658 + -325 = -649.461091658 x = -649.461091658 Simplifying x = -649.461091658Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.538908342, -649.461091658}
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