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Simplifying 66 + -5x = 5x2 Solving 66 + -5x = 5x2 Solving for variable 'x'. Combine like terms: 5x2 + -5x2 = 0 66 + -5x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -13.2 + x + x2 = 0 Move the constant term to the right: Add '13.2' to each side of the equation. -13.2 + x + 13.2 + x2 = 0 + 13.2 Reorder the terms: -13.2 + 13.2 + x + x2 = 0 + 13.2 Combine like terms: -13.2 + 13.2 = 0.0 0.0 + x + x2 = 0 + 13.2 x + x2 = 0 + 13.2 Combine like terms: 0 + 13.2 = 13.2 x + x2 = 13.2 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 = 13.2 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 13.2 + 0.25 Combine like terms: 13.2 + 0.25 = 13.45 1.25 + x2 = 13.45 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 13.45 Calculate the square root of the right side: 3.667424164 Break this problem into two subproblems by setting (x + 0.5) equal to 3.667424164 and -3.667424164.Subproblem 1
x + 0.5 = 3.667424164 Simplifying x + 0.5 = 3.667424164 Reorder the terms: 0.5 + x = 3.667424164 Solving 0.5 + x = 3.667424164 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 = 3.667424164 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.667424164 + -0.5 x = 3.667424164 + -0.5 Combine like terms: 3.667424164 + -0.5 = 3.167424164 x = 3.167424164 Simplifying x = 3.167424164Subproblem 2
x + 0.5 = -3.667424164 Simplifying x + 0.5 = -3.667424164 Reorder the terms: 0.5 + x = -3.667424164 Solving 0.5 + x = -3.667424164 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 = -3.667424164 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.667424164 + -0.5 x = -3.667424164 + -0.5 Combine like terms: -3.667424164 + -0.5 = -4.167424164 x = -4.167424164 Simplifying x = -4.167424164Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.167424164, -4.167424164}
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