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Simplifying 0.65 = x2 + -4x + 4 Reorder the terms: 0.65 = 4 + -4x + x2 Solving 0.65 = 4 + -4x + x2 Solving for variable 'x'. Combine like terms: 0.65 + -4 = -3.35 -3.35 + 4x + -1x2 = 4 + -4x + x2 + -4 + 4x + -1x2 Reorder the terms: -3.35 + 4x + -1x2 = 4 + -4 + -4x + 4x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -3.35 + 4x + -1x2 = 0 + -4x + 4x + x2 + -1x2 -3.35 + 4x + -1x2 = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -3.35 + 4x + -1x2 = 0 + x2 + -1x2 -3.35 + 4x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -3.35 + 4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3.35 + -4x + x2 = 0 Move the constant term to the right: Add '-3.35' to each side of the equation. 3.35 + -4x + -3.35 + x2 = 0 + -3.35 Reorder the terms: 3.35 + -3.35 + -4x + x2 = 0 + -3.35 Combine like terms: 3.35 + -3.35 = 0.00 0.00 + -4x + x2 = 0 + -3.35 -4x + x2 = 0 + -3.35 Combine like terms: 0 + -3.35 = -3.35 -4x + x2 = -3.35 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 = -3.35 + 4 Reorder the terms: 4 + -4x + x2 = -3.35 + 4 Combine like terms: -3.35 + 4 = 0.65 4 + -4x + x2 = 0.65 Factor a perfect square on the left side: (x + -2)(x + -2) = 0.65 Calculate the square root of the right side: 0.806225775 Break this problem into two subproblems by setting (x + -2) equal to 0.806225775 and -0.806225775.Subproblem 1
x + -2 = 0.806225775 Simplifying x + -2 = 0.806225775 Reorder the terms: -2 + x = 0.806225775 Solving -2 + x = 0.806225775 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 = 0.806225775 + 2 Combine like terms: -2 + 2 = 0 0 + x = 0.806225775 + 2 x = 0.806225775 + 2 Combine like terms: 0.806225775 + 2 = 2.806225775 x = 2.806225775 Simplifying x = 2.806225775Subproblem 2
x + -2 = -0.806225775 Simplifying x + -2 = -0.806225775 Reorder the terms: -2 + x = -0.806225775 Solving -2 + x = -0.806225775 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 = -0.806225775 + 2 Combine like terms: -2 + 2 = 0 0 + x = -0.806225775 + 2 x = -0.806225775 + 2 Combine like terms: -0.806225775 + 2 = 1.193774225 x = 1.193774225 Simplifying x = 1.193774225Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.806225775, 1.193774225}
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