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Simplifying 25x2 + 100x = -48 Reorder the terms: 100x + 25x2 = -48 Solving 100x + 25x2 = -48 Solving for variable 'x'. Reorder the terms: 48 + 100x + 25x2 = -48 + 48 Combine like terms: -48 + 48 = 0 48 + 100x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.92 + 4x + x2 = 0 Move the constant term to the right: Add '-1.92' to each side of the equation. 1.92 + 4x + -1.92 + x2 = 0 + -1.92 Reorder the terms: 1.92 + -1.92 + 4x + x2 = 0 + -1.92 Combine like terms: 1.92 + -1.92 = 0.00 0.00 + 4x + x2 = 0 + -1.92 4x + x2 = 0 + -1.92 Combine like terms: 0 + -1.92 = -1.92 4x + x2 = -1.92 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.92 + 4 Reorder the terms: 4 + 4x + x2 = -1.92 + 4 Combine like terms: -1.92 + 4 = 2.08 4 + 4x + x2 = 2.08 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.08 Calculate the square root of the right side: 1.44222051 Break this problem into two subproblems by setting (x + 2) equal to 1.44222051 and -1.44222051.Subproblem 1
x + 2 = 1.44222051 Simplifying x + 2 = 1.44222051 Reorder the terms: 2 + x = 1.44222051 Solving 2 + x = 1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.44222051 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.44222051 + -2 x = 1.44222051 + -2 Combine like terms: 1.44222051 + -2 = -0.55777949 x = -0.55777949 Simplifying x = -0.55777949Subproblem 2
x + 2 = -1.44222051 Simplifying x + 2 = -1.44222051 Reorder the terms: 2 + x = -1.44222051 Solving 2 + x = -1.44222051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.44222051 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.44222051 + -2 x = -1.44222051 + -2 Combine like terms: -1.44222051 + -2 = -3.44222051 x = -3.44222051 Simplifying x = -3.44222051Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.55777949, -3.44222051}
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