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Simplifying 25x2 + 20x + -92 = 0 Reorder the terms: -92 + 20x + 25x2 = 0 Solving -92 + 20x + 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'. -3.68 + 0.8x + x2 = 0 Move the constant term to the right: Add '3.68' to each side of the equation. -3.68 + 0.8x + 3.68 + x2 = 0 + 3.68 Reorder the terms: -3.68 + 3.68 + 0.8x + x2 = 0 + 3.68 Combine like terms: -3.68 + 3.68 = 0.00 0.00 + 0.8x + x2 = 0 + 3.68 0.8x + x2 = 0 + 3.68 Combine like terms: 0 + 3.68 = 3.68 0.8x + x2 = 3.68 The x term is 0.8x. Take half its coefficient (0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. 0.8x + 0.16 + x2 = 3.68 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 3.68 + 0.16 Combine like terms: 3.68 + 0.16 = 3.84 0.16 + 0.8x + x2 = 3.84 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3.84 Calculate the square root of the right side: 1.959591794 Break this problem into two subproblems by setting (x + 0.4) equal to 1.959591794 and -1.959591794.Subproblem 1
x + 0.4 = 1.959591794 Simplifying x + 0.4 = 1.959591794 Reorder the terms: 0.4 + x = 1.959591794 Solving 0.4 + x = 1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.959591794 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.959591794 + -0.4 x = 1.959591794 + -0.4 Combine like terms: 1.959591794 + -0.4 = 1.559591794 x = 1.559591794 Simplifying x = 1.559591794Subproblem 2
x + 0.4 = -1.959591794 Simplifying x + 0.4 = -1.959591794 Reorder the terms: 0.4 + x = -1.959591794 Solving 0.4 + x = -1.959591794 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.959591794 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.959591794 + -0.4 x = -1.959591794 + -0.4 Combine like terms: -1.959591794 + -0.4 = -2.359591794 x = -2.359591794 Simplifying x = -2.359591794Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.559591794, -2.359591794}
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