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Simplifying 4x2 + 43x + -40 = 0 Reorder the terms: -40 + 43x + 4x2 = 0 Solving -40 + 43x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -10 + 10.75x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 10.75x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 10.75x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 10.75x + x2 = 0 + 10 10.75x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 10.75x + x2 = 10 The x term is 10.75x. Take half its coefficient (5.375). Square it (28.890625) and add it to both sides. Add '28.890625' to each side of the equation. 10.75x + 28.890625 + x2 = 10 + 28.890625 Reorder the terms: 28.890625 + 10.75x + x2 = 10 + 28.890625 Combine like terms: 10 + 28.890625 = 38.890625 28.890625 + 10.75x + x2 = 38.890625 Factor a perfect square on the left side: (x + 5.375)(x + 5.375) = 38.890625 Calculate the square root of the right side: 6.236234842 Break this problem into two subproblems by setting (x + 5.375) equal to 6.236234842 and -6.236234842.Subproblem 1
x + 5.375 = 6.236234842 Simplifying x + 5.375 = 6.236234842 Reorder the terms: 5.375 + x = 6.236234842 Solving 5.375 + x = 6.236234842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = 6.236234842 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = 6.236234842 + -5.375 x = 6.236234842 + -5.375 Combine like terms: 6.236234842 + -5.375 = 0.861234842 x = 0.861234842 Simplifying x = 0.861234842Subproblem 2
x + 5.375 = -6.236234842 Simplifying x + 5.375 = -6.236234842 Reorder the terms: 5.375 + x = -6.236234842 Solving 5.375 + x = -6.236234842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.375' to each side of the equation. 5.375 + -5.375 + x = -6.236234842 + -5.375 Combine like terms: 5.375 + -5.375 = 0.000 0.000 + x = -6.236234842 + -5.375 x = -6.236234842 + -5.375 Combine like terms: -6.236234842 + -5.375 = -11.611234842 x = -11.611234842 Simplifying x = -11.611234842Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.861234842, -11.611234842}
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