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Simplifying 4x2 + 4x + 1 = 50 Reorder the terms: 1 + 4x + 4x2 = 50 Solving 1 + 4x + 4x2 = 50 Solving for variable 'x'. Reorder the terms: 1 + -50 + 4x + 4x2 = 50 + -50 Combine like terms: 1 + -50 = -49 -49 + 4x + 4x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -49 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + x + x2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + x + 12.25 + x2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + x + x2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + x + x2 = 0 + 12.25 x + x2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 x + x2 = 12.25 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. + 0.25 + x2 = 12.25 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 12.25 + 0.25 Combine like terms: 12.25 + 0.25 = 12.5 1.25 + x2 = 12.5 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + 0.5) equal to 3.535533906 and -3.535533906.Subproblem 1
x + 0.5 = 3.535533906 Simplifying x + 0.5 = 3.535533906 Reorder the terms: 0.5 + x = 3.535533906 Solving 0.5 + x = 3.535533906 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 = 3.535533906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.535533906 + -0.5 x = 3.535533906 + -0.5 Combine like terms: 3.535533906 + -0.5 = 3.035533906 x = 3.035533906 Simplifying x = 3.035533906Subproblem 2
x + 0.5 = -3.535533906 Simplifying x + 0.5 = -3.535533906 Reorder the terms: 0.5 + x = -3.535533906 Solving 0.5 + x = -3.535533906 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 = -3.535533906 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.535533906 + -0.5 x = -3.535533906 + -0.5 Combine like terms: -3.535533906 + -0.5 = -4.035533906 x = -4.035533906 Simplifying x = -4.035533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.035533906, -4.035533906}
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