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Simplifying 5x2 + -5.5x + -5 = 0 Reorder the terms: -5 + -5.5x + 5x2 = 0 Solving -5 + -5.5x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + -1.1x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -1.1x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1.1x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1.1x + x2 = 0 + 1 -1.1x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1.1x + x2 = 1 The x term is -1.1x. Take half its coefficient (-0.55). Square it (0.3025) and add it to both sides. Add '0.3025' to each side of the equation. -1.1x + 0.3025 + x2 = 1 + 0.3025 Reorder the terms: 0.3025 + -1.1x + x2 = 1 + 0.3025 Combine like terms: 1 + 0.3025 = 1.3025 0.3025 + -1.1x + x2 = 1.3025 Factor a perfect square on the left side: (x + -0.55)(x + -0.55) = 1.3025 Calculate the square root of the right side: 1.141271221 Break this problem into two subproblems by setting (x + -0.55) equal to 1.141271221 and -1.141271221.Subproblem 1
x + -0.55 = 1.141271221 Simplifying x + -0.55 = 1.141271221 Reorder the terms: -0.55 + x = 1.141271221 Solving -0.55 + x = 1.141271221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = 1.141271221 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = 1.141271221 + 0.55 x = 1.141271221 + 0.55 Combine like terms: 1.141271221 + 0.55 = 1.691271221 x = 1.691271221 Simplifying x = 1.691271221Subproblem 2
x + -0.55 = -1.141271221 Simplifying x + -0.55 = -1.141271221 Reorder the terms: -0.55 + x = -1.141271221 Solving -0.55 + x = -1.141271221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.55' to each side of the equation. -0.55 + 0.55 + x = -1.141271221 + 0.55 Combine like terms: -0.55 + 0.55 = 0.00 0.00 + x = -1.141271221 + 0.55 x = -1.141271221 + 0.55 Combine like terms: -1.141271221 + 0.55 = -0.591271221 x = -0.591271221 Simplifying x = -0.591271221Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.691271221, -0.591271221}
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