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Simplifying 25x2 + -30x + -3 = 0 Reorder the terms: -3 + -30x + 25x2 = 0 Solving -3 + -30x + 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'. -0.12 + -1.2x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -1.2x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -1.2x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -1.2x + x2 = 0 + 0.12 -1.2x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -1.2x + x2 = 0.12 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 0.12 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 0.12 + 0.36 Combine like terms: 0.12 + 0.36 = 0.48 0.36 + -1.2x + x2 = 0.48 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + -0.6) equal to 0.692820323 and -0.692820323.Subproblem 1
x + -0.6 = 0.692820323 Simplifying x + -0.6 = 0.692820323 Reorder the terms: -0.6 + x = 0.692820323 Solving -0.6 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 0.692820323 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.692820323 + 0.6 x = 0.692820323 + 0.6 Combine like terms: 0.692820323 + 0.6 = 1.292820323 x = 1.292820323 Simplifying x = 1.292820323Subproblem 2
x + -0.6 = -0.692820323 Simplifying x + -0.6 = -0.692820323 Reorder the terms: -0.6 + x = -0.692820323 Solving -0.6 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -0.692820323 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.692820323 + 0.6 x = -0.692820323 + 0.6 Combine like terms: -0.692820323 + 0.6 = -0.092820323 x = -0.092820323 Simplifying x = -0.092820323Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.292820323, -0.092820323}
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