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Simplifying 10x + 44x2 = 0.6 Solving 10x + 44x2 = 0.6 Solving for variable 'x'. Reorder the terms: -0.6 + 10x + 44x2 = 0.6 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 -0.6 + 10x + 44x2 = 0.0 Begin completing the square. Divide all terms by 44 the coefficient of the squared term: Divide each side by '44'. -0.01363636364 + 0.2272727273x + x2 = 0.0 Move the constant term to the right: Add '0.01363636364' to each side of the equation. -0.01363636364 + 0.2272727273x + 0.01363636364 + x2 = 0.0 + 0.01363636364 Reorder the terms: -0.01363636364 + 0.01363636364 + 0.2272727273x + x2 = 0.0 + 0.01363636364 Combine like terms: -0.01363636364 + 0.01363636364 = 0.00000000000 0.00000000000 + 0.2272727273x + x2 = 0.0 + 0.01363636364 0.2272727273x + x2 = 0.0 + 0.01363636364 Combine like terms: 0.0 + 0.01363636364 = 0.01363636364 0.2272727273x + x2 = 0.01363636364 The x term is 0.2272727273x. Take half its coefficient (0.1136363637). Square it (0.01291322316) and add it to both sides. Add '0.01291322316' to each side of the equation. 0.2272727273x + 0.01291322316 + x2 = 0.01363636364 + 0.01291322316 Reorder the terms: 0.01291322316 + 0.2272727273x + x2 = 0.01363636364 + 0.01291322316 Combine like terms: 0.01363636364 + 0.01291322316 = 0.0265495868 0.01291322316 + 0.2272727273x + x2 = 0.0265495868 Factor a perfect square on the left side: (x + 0.1136363637)(x + 0.1136363637) = 0.0265495868 Calculate the square root of the right side: 0.162940439 Break this problem into two subproblems by setting (x + 0.1136363637) equal to 0.162940439 and -0.162940439.Subproblem 1
x + 0.1136363637 = 0.162940439 Simplifying x + 0.1136363637 = 0.162940439 Reorder the terms: 0.1136363637 + x = 0.162940439 Solving 0.1136363637 + x = 0.162940439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1136363637' to each side of the equation. 0.1136363637 + -0.1136363637 + x = 0.162940439 + -0.1136363637 Combine like terms: 0.1136363637 + -0.1136363637 = 0.0000000000 0.0000000000 + x = 0.162940439 + -0.1136363637 x = 0.162940439 + -0.1136363637 Combine like terms: 0.162940439 + -0.1136363637 = 0.0493040753 x = 0.0493040753 Simplifying x = 0.0493040753Subproblem 2
x + 0.1136363637 = -0.162940439 Simplifying x + 0.1136363637 = -0.162940439 Reorder the terms: 0.1136363637 + x = -0.162940439 Solving 0.1136363637 + x = -0.162940439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1136363637' to each side of the equation. 0.1136363637 + -0.1136363637 + x = -0.162940439 + -0.1136363637 Combine like terms: 0.1136363637 + -0.1136363637 = 0.0000000000 0.0000000000 + x = -0.162940439 + -0.1136363637 x = -0.162940439 + -0.1136363637 Combine like terms: -0.162940439 + -0.1136363637 = -0.2765768027 x = -0.2765768027 Simplifying x = -0.2765768027Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0493040753, -0.2765768027}
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