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Simplifying 8x2 + 79x + 35 = 0 Reorder the terms: 35 + 79x + 8x2 = 0 Solving 35 + 79x + 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'. 4.375 + 9.875x + x2 = 0 Move the constant term to the right: Add '-4.375' to each side of the equation. 4.375 + 9.875x + -4.375 + x2 = 0 + -4.375 Reorder the terms: 4.375 + -4.375 + 9.875x + x2 = 0 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + 9.875x + x2 = 0 + -4.375 9.875x + x2 = 0 + -4.375 Combine like terms: 0 + -4.375 = -4.375 9.875x + x2 = -4.375 The x term is 9.875x. Take half its coefficient (4.9375). Square it (24.37890625) and add it to both sides. Add '24.37890625' to each side of the equation. 9.875x + 24.37890625 + x2 = -4.375 + 24.37890625 Reorder the terms: 24.37890625 + 9.875x + x2 = -4.375 + 24.37890625 Combine like terms: -4.375 + 24.37890625 = 20.00390625 24.37890625 + 9.875x + x2 = 20.00390625 Factor a perfect square on the left side: (x + 4.9375)(x + 4.9375) = 20.00390625 Calculate the square root of the right side: 4.472572666 Break this problem into two subproblems by setting (x + 4.9375) equal to 4.472572666 and -4.472572666.Subproblem 1
x + 4.9375 = 4.472572666 Simplifying x + 4.9375 = 4.472572666 Reorder the terms: 4.9375 + x = 4.472572666 Solving 4.9375 + x = 4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9375' to each side of the equation. 4.9375 + -4.9375 + x = 4.472572666 + -4.9375 Combine like terms: 4.9375 + -4.9375 = 0.0000 0.0000 + x = 4.472572666 + -4.9375 x = 4.472572666 + -4.9375 Combine like terms: 4.472572666 + -4.9375 = -0.464927334 x = -0.464927334 Simplifying x = -0.464927334Subproblem 2
x + 4.9375 = -4.472572666 Simplifying x + 4.9375 = -4.472572666 Reorder the terms: 4.9375 + x = -4.472572666 Solving 4.9375 + x = -4.472572666 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.9375' to each side of the equation. 4.9375 + -4.9375 + x = -4.472572666 + -4.9375 Combine like terms: 4.9375 + -4.9375 = 0.0000 0.0000 + x = -4.472572666 + -4.9375 x = -4.472572666 + -4.9375 Combine like terms: -4.472572666 + -4.9375 = -9.410072666 x = -9.410072666 Simplifying x = -9.410072666Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.464927334, -9.410072666}
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