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Simplifying 25x2 + -30x + 0.6 = 0 Reorder the terms: 0.6 + -30x + 25x2 = 0 Solving 0.6 + -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'. 0.024 + -1.2x + x2 = 0 Move the constant term to the right: Add '-0.024' to each side of the equation. 0.024 + -1.2x + -0.024 + x2 = 0 + -0.024 Reorder the terms: 0.024 + -0.024 + -1.2x + x2 = 0 + -0.024 Combine like terms: 0.024 + -0.024 = 0.000 0.000 + -1.2x + x2 = 0 + -0.024 -1.2x + x2 = 0 + -0.024 Combine like terms: 0 + -0.024 = -0.024 -1.2x + x2 = -0.024 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 = -0.024 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = -0.024 + 0.36 Combine like terms: -0.024 + 0.36 = 0.336 0.36 + -1.2x + x2 = 0.336 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 0.336 Calculate the square root of the right side: 0.57965507 Break this problem into two subproblems by setting (x + -0.6) equal to 0.57965507 and -0.57965507.Subproblem 1
x + -0.6 = 0.57965507 Simplifying x + -0.6 = 0.57965507 Reorder the terms: -0.6 + x = 0.57965507 Solving -0.6 + x = 0.57965507 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 = 0.57965507 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 0.57965507 + 0.6 x = 0.57965507 + 0.6 Combine like terms: 0.57965507 + 0.6 = 1.17965507 x = 1.17965507 Simplifying x = 1.17965507Subproblem 2
x + -0.6 = -0.57965507 Simplifying x + -0.6 = -0.57965507 Reorder the terms: -0.6 + x = -0.57965507 Solving -0.6 + x = -0.57965507 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 = -0.57965507 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -0.57965507 + 0.6 x = -0.57965507 + 0.6 Combine like terms: -0.57965507 + 0.6 = 0.02034493 x = 0.02034493 Simplifying x = 0.02034493Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.17965507, 0.02034493}
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