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Simplifying 25x2 + -48x + 4 = 0 Reorder the terms: 4 + -48x + 25x2 = 0 Solving 4 + -48x + 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'. 0.16 + -1.92x + x2 = 0 Move the constant term to the right: Add '-0.16' to each side of the equation. 0.16 + -1.92x + -0.16 + x2 = 0 + -0.16 Reorder the terms: 0.16 + -0.16 + -1.92x + x2 = 0 + -0.16 Combine like terms: 0.16 + -0.16 = 0.00 0.00 + -1.92x + x2 = 0 + -0.16 -1.92x + x2 = 0 + -0.16 Combine like terms: 0 + -0.16 = -0.16 -1.92x + x2 = -0.16 The x term is -1.92x. Take half its coefficient (-0.96). Square it (0.9216) and add it to both sides. Add '0.9216' to each side of the equation. -1.92x + 0.9216 + x2 = -0.16 + 0.9216 Reorder the terms: 0.9216 + -1.92x + x2 = -0.16 + 0.9216 Combine like terms: -0.16 + 0.9216 = 0.7616 0.9216 + -1.92x + x2 = 0.7616 Factor a perfect square on the left side: (x + -0.96)(x + -0.96) = 0.7616 Calculate the square root of the right side: 0.872696969 Break this problem into two subproblems by setting (x + -0.96) equal to 0.872696969 and -0.872696969.Subproblem 1
x + -0.96 = 0.872696969 Simplifying x + -0.96 = 0.872696969 Reorder the terms: -0.96 + x = 0.872696969 Solving -0.96 + x = 0.872696969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96' to each side of the equation. -0.96 + 0.96 + x = 0.872696969 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + x = 0.872696969 + 0.96 x = 0.872696969 + 0.96 Combine like terms: 0.872696969 + 0.96 = 1.832696969 x = 1.832696969 Simplifying x = 1.832696969Subproblem 2
x + -0.96 = -0.872696969 Simplifying x + -0.96 = -0.872696969 Reorder the terms: -0.96 + x = -0.872696969 Solving -0.96 + x = -0.872696969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.96' to each side of the equation. -0.96 + 0.96 + x = -0.872696969 + 0.96 Combine like terms: -0.96 + 0.96 = 0.00 0.00 + x = -0.872696969 + 0.96 x = -0.872696969 + 0.96 Combine like terms: -0.872696969 + 0.96 = 0.087303031 x = 0.087303031 Simplifying x = 0.087303031Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.832696969, 0.087303031}
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