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Simplifying 4x2 + -4 + 6x2 + x + 1 = 180 Reorder the terms: -4 + 1 + x + 4x2 + 6x2 = 180 Combine like terms: -4 + 1 = -3 -3 + x + 4x2 + 6x2 = 180 Combine like terms: 4x2 + 6x2 = 10x2 -3 + x + 10x2 = 180 Solving -3 + x + 10x2 = 180 Solving for variable 'x'. Reorder the terms: -3 + -180 + x + 10x2 = 180 + -180 Combine like terms: -3 + -180 = -183 -183 + x + 10x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -183 + x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -18.3 + 0.1x + x2 = 0.0 Move the constant term to the right: Add '18.3' to each side of the equation. -18.3 + 0.1x + 18.3 + x2 = 0.0 + 18.3 Reorder the terms: -18.3 + 18.3 + 0.1x + x2 = 0.0 + 18.3 Combine like terms: -18.3 + 18.3 = 0.0 0.0 + 0.1x + x2 = 0.0 + 18.3 0.1x + x2 = 0.0 + 18.3 Combine like terms: 0.0 + 18.3 = 18.3 0.1x + x2 = 18.3 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.1x + 0.25 + x2 = 18.3 + 0.25 Reorder the terms: 0.25 + 0.1x + x2 = 18.3 + 0.25 Combine like terms: 18.3 + 0.25 = 18.55 0.25 + 0.1x + x2 = 18.55 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 18.55 Calculate the square root of the right side: 4.306971093 Break this problem into two subproblems by setting (x + 0.5) equal to 4.306971093 and -4.306971093.Subproblem 1
x + 0.5 = 4.306971093 Simplifying x + 0.5 = 4.306971093 Reorder the terms: 0.5 + x = 4.306971093 Solving 0.5 + x = 4.306971093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.306971093 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.306971093 + -0.5 x = 4.306971093 + -0.5 Combine like terms: 4.306971093 + -0.5 = 3.806971093 x = 3.806971093 Simplifying x = 3.806971093Subproblem 2
x + 0.5 = -4.306971093 Simplifying x + 0.5 = -4.306971093 Reorder the terms: 0.5 + x = -4.306971093 Solving 0.5 + x = -4.306971093 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.306971093 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.306971093 + -0.5 x = -4.306971093 + -0.5 Combine like terms: -4.306971093 + -0.5 = -4.806971093 x = -4.806971093 Simplifying x = -4.806971093Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.806971093, -4.806971093}
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