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Simplifying 4x2 + 3x + -160 = 0 Reorder the terms: -160 + 3x + 4x2 = 0 Solving -160 + 3x + 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'. -40 + 0.75x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 0.75x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 0.75x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 0.75x + x2 = 0 + 40 0.75x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 0.75x + x2 = 40 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 40 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 40 + 0.140625 Combine like terms: 40 + 0.140625 = 40.140625 0.140625 + 0.75x + x2 = 40.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 40.140625 Calculate the square root of the right side: 6.335662949 Break this problem into two subproblems by setting (x + 0.375) equal to 6.335662949 and -6.335662949.Subproblem 1
x + 0.375 = 6.335662949 Simplifying x + 0.375 = 6.335662949 Reorder the terms: 0.375 + x = 6.335662949 Solving 0.375 + x = 6.335662949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 6.335662949 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 6.335662949 + -0.375 x = 6.335662949 + -0.375 Combine like terms: 6.335662949 + -0.375 = 5.960662949 x = 5.960662949 Simplifying x = 5.960662949Subproblem 2
x + 0.375 = -6.335662949 Simplifying x + 0.375 = -6.335662949 Reorder the terms: 0.375 + x = -6.335662949 Solving 0.375 + x = -6.335662949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -6.335662949 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -6.335662949 + -0.375 x = -6.335662949 + -0.375 Combine like terms: -6.335662949 + -0.375 = -6.710662949 x = -6.710662949 Simplifying x = -6.710662949Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.960662949, -6.710662949}
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