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Simplifying 8x2 + 15x + -41 = 0 Reorder the terms: -41 + 15x + 8x2 = 0 Solving -41 + 15x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -5.125 + 1.875x + x2 = 0 Move the constant term to the right: Add '5.125' to each side of the equation. -5.125 + 1.875x + 5.125 + x2 = 0 + 5.125 Reorder the terms: -5.125 + 5.125 + 1.875x + x2 = 0 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + 1.875x + x2 = 0 + 5.125 1.875x + x2 = 0 + 5.125 Combine like terms: 0 + 5.125 = 5.125 1.875x + x2 = 5.125 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = 5.125 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = 5.125 + 0.87890625 Combine like terms: 5.125 + 0.87890625 = 6.00390625 0.87890625 + 1.875x + x2 = 6.00390625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 6.00390625 Calculate the square root of the right side: 2.450286973 Break this problem into two subproblems by setting (x + 0.9375) equal to 2.450286973 and -2.450286973.Subproblem 1
x + 0.9375 = 2.450286973 Simplifying x + 0.9375 = 2.450286973 Reorder the terms: 0.9375 + x = 2.450286973 Solving 0.9375 + x = 2.450286973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 2.450286973 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 2.450286973 + -0.9375 x = 2.450286973 + -0.9375 Combine like terms: 2.450286973 + -0.9375 = 1.512786973 x = 1.512786973 Simplifying x = 1.512786973Subproblem 2
x + 0.9375 = -2.450286973 Simplifying x + 0.9375 = -2.450286973 Reorder the terms: 0.9375 + x = -2.450286973 Solving 0.9375 + x = -2.450286973 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -2.450286973 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -2.450286973 + -0.9375 x = -2.450286973 + -0.9375 Combine like terms: -2.450286973 + -0.9375 = -3.387786973 x = -3.387786973 Simplifying x = -3.387786973Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.512786973, -3.387786973}
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