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Simplifying 5x2 + -7.7x + -1.8 = 0 Reorder the terms: -1.8 + -7.7x + 5x2 = 0 Solving -1.8 + -7.7x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.36 + -1.54x + x2 = 0 Move the constant term to the right: Add '0.36' to each side of the equation. -0.36 + -1.54x + 0.36 + x2 = 0 + 0.36 Reorder the terms: -0.36 + 0.36 + -1.54x + x2 = 0 + 0.36 Combine like terms: -0.36 + 0.36 = 0.00 0.00 + -1.54x + x2 = 0 + 0.36 -1.54x + x2 = 0 + 0.36 Combine like terms: 0 + 0.36 = 0.36 -1.54x + x2 = 0.36 The x term is -1.54x. Take half its coefficient (-0.77). Square it (0.5929) and add it to both sides. Add '0.5929' to each side of the equation. -1.54x + 0.5929 + x2 = 0.36 + 0.5929 Reorder the terms: 0.5929 + -1.54x + x2 = 0.36 + 0.5929 Combine like terms: 0.36 + 0.5929 = 0.9529 0.5929 + -1.54x + x2 = 0.9529 Factor a perfect square on the left side: (x + -0.77)(x + -0.77) = 0.9529 Calculate the square root of the right side: 0.976165969 Break this problem into two subproblems by setting (x + -0.77) equal to 0.976165969 and -0.976165969.Subproblem 1
x + -0.77 = 0.976165969 Simplifying x + -0.77 = 0.976165969 Reorder the terms: -0.77 + x = 0.976165969 Solving -0.77 + x = 0.976165969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.77' to each side of the equation. -0.77 + 0.77 + x = 0.976165969 + 0.77 Combine like terms: -0.77 + 0.77 = 0.00 0.00 + x = 0.976165969 + 0.77 x = 0.976165969 + 0.77 Combine like terms: 0.976165969 + 0.77 = 1.746165969 x = 1.746165969 Simplifying x = 1.746165969Subproblem 2
x + -0.77 = -0.976165969 Simplifying x + -0.77 = -0.976165969 Reorder the terms: -0.77 + x = -0.976165969 Solving -0.77 + x = -0.976165969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.77' to each side of the equation. -0.77 + 0.77 + x = -0.976165969 + 0.77 Combine like terms: -0.77 + 0.77 = 0.00 0.00 + x = -0.976165969 + 0.77 x = -0.976165969 + 0.77 Combine like terms: -0.976165969 + 0.77 = -0.206165969 x = -0.206165969 Simplifying x = -0.206165969Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.746165969, -0.206165969}
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