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Simplifying 25x2 + -29x + -6 = 0 Reorder the terms: -6 + -29x + 25x2 = 0 Solving -6 + -29x + 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'. -0.24 + -1.16x + x2 = 0 Move the constant term to the right: Add '0.24' to each side of the equation. -0.24 + -1.16x + 0.24 + x2 = 0 + 0.24 Reorder the terms: -0.24 + 0.24 + -1.16x + x2 = 0 + 0.24 Combine like terms: -0.24 + 0.24 = 0.00 0.00 + -1.16x + x2 = 0 + 0.24 -1.16x + x2 = 0 + 0.24 Combine like terms: 0 + 0.24 = 0.24 -1.16x + x2 = 0.24 The x term is -1.16x. Take half its coefficient (-0.58). Square it (0.3364) and add it to both sides. Add '0.3364' to each side of the equation. -1.16x + 0.3364 + x2 = 0.24 + 0.3364 Reorder the terms: 0.3364 + -1.16x + x2 = 0.24 + 0.3364 Combine like terms: 0.24 + 0.3364 = 0.5764 0.3364 + -1.16x + x2 = 0.5764 Factor a perfect square on the left side: (x + -0.58)(x + -0.58) = 0.5764 Calculate the square root of the right side: 0.759210116 Break this problem into two subproblems by setting (x + -0.58) equal to 0.759210116 and -0.759210116.Subproblem 1
x + -0.58 = 0.759210116 Simplifying x + -0.58 = 0.759210116 Reorder the terms: -0.58 + x = 0.759210116 Solving -0.58 + x = 0.759210116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = 0.759210116 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = 0.759210116 + 0.58 x = 0.759210116 + 0.58 Combine like terms: 0.759210116 + 0.58 = 1.339210116 x = 1.339210116 Simplifying x = 1.339210116Subproblem 2
x + -0.58 = -0.759210116 Simplifying x + -0.58 = -0.759210116 Reorder the terms: -0.58 + x = -0.759210116 Solving -0.58 + x = -0.759210116 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.58' to each side of the equation. -0.58 + 0.58 + x = -0.759210116 + 0.58 Combine like terms: -0.58 + 0.58 = 0.00 0.00 + x = -0.759210116 + 0.58 x = -0.759210116 + 0.58 Combine like terms: -0.759210116 + 0.58 = -0.179210116 x = -0.179210116 Simplifying x = -0.179210116Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.339210116, -0.179210116}
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