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Simplifying 25x2 + 20x + -76 = 0 Reorder the terms: -76 + 20x + 25x2 = 0 Solving -76 + 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'. -3.04 + 0.8x + x2 = 0 Move the constant term to the right: Add '3.04' to each side of the equation. -3.04 + 0.8x + 3.04 + x2 = 0 + 3.04 Reorder the terms: -3.04 + 3.04 + 0.8x + x2 = 0 + 3.04 Combine like terms: -3.04 + 3.04 = 0.00 0.00 + 0.8x + x2 = 0 + 3.04 0.8x + x2 = 0 + 3.04 Combine like terms: 0 + 3.04 = 3.04 0.8x + x2 = 3.04 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 = 3.04 + 0.16 Reorder the terms: 0.16 + 0.8x + x2 = 3.04 + 0.16 Combine like terms: 3.04 + 0.16 = 3.2 0.16 + 0.8x + x2 = 3.2 Factor a perfect square on the left side: (x + 0.4)(x + 0.4) = 3.2 Calculate the square root of the right side: 1.788854382 Break this problem into two subproblems by setting (x + 0.4) equal to 1.788854382 and -1.788854382.Subproblem 1
x + 0.4 = 1.788854382 Simplifying x + 0.4 = 1.788854382 Reorder the terms: 0.4 + x = 1.788854382 Solving 0.4 + x = 1.788854382 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 = 1.788854382 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.788854382 + -0.4 x = 1.788854382 + -0.4 Combine like terms: 1.788854382 + -0.4 = 1.388854382 x = 1.388854382 Simplifying x = 1.388854382Subproblem 2
x + 0.4 = -1.788854382 Simplifying x + 0.4 = -1.788854382 Reorder the terms: 0.4 + x = -1.788854382 Solving 0.4 + x = -1.788854382 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 = -1.788854382 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.788854382 + -0.4 x = -1.788854382 + -0.4 Combine like terms: -1.788854382 + -0.4 = -2.188854382 x = -2.188854382 Simplifying x = -2.188854382Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.388854382, -2.188854382}
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