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Simplifying 25x2 + 66x + -110 = 0 Reorder the terms: -110 + 66x + 25x2 = 0 Solving -110 + 66x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -4.4 + 2.64x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 2.64x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 2.64x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 2.64x + x2 = 0 + 4.4 2.64x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 2.64x + x2 = 4.4 The x term is 2.64x. Take half its coefficient (1.32). Square it (1.7424) and add it to both sides. Add '1.7424' to each side of the equation. 2.64x + 1.7424 + x2 = 4.4 + 1.7424 Reorder the terms: 1.7424 + 2.64x + x2 = 4.4 + 1.7424 Combine like terms: 4.4 + 1.7424 = 6.1424 1.7424 + 2.64x + x2 = 6.1424 Factor a perfect square on the left side: (x + 1.32)(x + 1.32) = 6.1424 Calculate the square root of the right side: 2.478386572 Break this problem into two subproblems by setting (x + 1.32) equal to 2.478386572 and -2.478386572.Subproblem 1
x + 1.32 = 2.478386572 Simplifying x + 1.32 = 2.478386572 Reorder the terms: 1.32 + x = 2.478386572 Solving 1.32 + x = 2.478386572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.32' to each side of the equation. 1.32 + -1.32 + x = 2.478386572 + -1.32 Combine like terms: 1.32 + -1.32 = 0.00 0.00 + x = 2.478386572 + -1.32 x = 2.478386572 + -1.32 Combine like terms: 2.478386572 + -1.32 = 1.158386572 x = 1.158386572 Simplifying x = 1.158386572Subproblem 2
x + 1.32 = -2.478386572 Simplifying x + 1.32 = -2.478386572 Reorder the terms: 1.32 + x = -2.478386572 Solving 1.32 + x = -2.478386572 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.32' to each side of the equation. 1.32 + -1.32 + x = -2.478386572 + -1.32 Combine like terms: 1.32 + -1.32 = 0.00 0.00 + x = -2.478386572 + -1.32 x = -2.478386572 + -1.32 Combine like terms: -2.478386572 + -1.32 = -3.798386572 x = -3.798386572 Simplifying x = -3.798386572Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.158386572, -3.798386572}
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