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Simplifying -1.2x2 + x = -25 Reorder the terms: x + -1.2x2 = -25 Solving x + -1.2x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + x + -1.2x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + x + -1.2x2 = 0 Begin completing the square. Divide all terms by -1.2 the coefficient of the squared term: Divide each side by '-1.2'. -20.83333333 + -0.8333333333x + x2 = 0 Move the constant term to the right: Add '20.83333333' to each side of the equation. -20.83333333 + -0.8333333333x + 20.83333333 + x2 = 0 + 20.83333333 Reorder the terms: -20.83333333 + 20.83333333 + -0.8333333333x + x2 = 0 + 20.83333333 Combine like terms: -20.83333333 + 20.83333333 = 0.00000000 0.00000000 + -0.8333333333x + x2 = 0 + 20.83333333 -0.8333333333x + x2 = 0 + 20.83333333 Combine like terms: 0 + 20.83333333 = 20.83333333 -0.8333333333x + x2 = 20.83333333 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.8333333333x + 0.25 + x2 = 20.83333333 + 0.25 Reorder the terms: 0.25 + -0.8333333333x + x2 = 20.83333333 + 0.25 Combine like terms: 20.83333333 + 0.25 = 21.08333333 0.25 + -0.8333333333x + x2 = 21.08333333 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 21.08333333 Calculate the square root of the right side: 4.591659104 Break this problem into two subproblems by setting (x + 0.5) equal to 4.591659104 and -4.591659104.Subproblem 1
x + 0.5 = 4.591659104 Simplifying x + 0.5 = 4.591659104 Reorder the terms: 0.5 + x = 4.591659104 Solving 0.5 + x = 4.591659104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 4.591659104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.591659104 + -0.5 x = 4.591659104 + -0.5 Combine like terms: 4.591659104 + -0.5 = 4.091659104 x = 4.091659104 Simplifying x = 4.091659104Subproblem 2
x + 0.5 = -4.591659104 Simplifying x + 0.5 = -4.591659104 Reorder the terms: 0.5 + x = -4.591659104 Solving 0.5 + x = -4.591659104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -4.591659104 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.591659104 + -0.5 x = -4.591659104 + -0.5 Combine like terms: -4.591659104 + -0.5 = -5.091659104 x = -5.091659104 Simplifying x = -5.091659104Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.091659104, -5.091659104}
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