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Simplifying 5x2 + -44x + 88 = 0 Reorder the terms: 88 + -44x + 5x2 = 0 Solving 88 + -44x + 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'. 17.6 + -8.8x + x2 = 0 Move the constant term to the right: Add '-17.6' to each side of the equation. 17.6 + -8.8x + -17.6 + x2 = 0 + -17.6 Reorder the terms: 17.6 + -17.6 + -8.8x + x2 = 0 + -17.6 Combine like terms: 17.6 + -17.6 = 0.0 0.0 + -8.8x + x2 = 0 + -17.6 -8.8x + x2 = 0 + -17.6 Combine like terms: 0 + -17.6 = -17.6 -8.8x + x2 = -17.6 The x term is -8.8x. Take half its coefficient (-4.4). Square it (19.36) and add it to both sides. Add '19.36' to each side of the equation. -8.8x + 19.36 + x2 = -17.6 + 19.36 Reorder the terms: 19.36 + -8.8x + x2 = -17.6 + 19.36 Combine like terms: -17.6 + 19.36 = 1.76 19.36 + -8.8x + x2 = 1.76 Factor a perfect square on the left side: (x + -4.4)(x + -4.4) = 1.76 Calculate the square root of the right side: 1.326649916 Break this problem into two subproblems by setting (x + -4.4) equal to 1.326649916 and -1.326649916.Subproblem 1
x + -4.4 = 1.326649916 Simplifying x + -4.4 = 1.326649916 Reorder the terms: -4.4 + x = 1.326649916 Solving -4.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = 1.326649916 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = 1.326649916 + 4.4 x = 1.326649916 + 4.4 Combine like terms: 1.326649916 + 4.4 = 5.726649916 x = 5.726649916 Simplifying x = 5.726649916Subproblem 2
x + -4.4 = -1.326649916 Simplifying x + -4.4 = -1.326649916 Reorder the terms: -4.4 + x = -1.326649916 Solving -4.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.4' to each side of the equation. -4.4 + 4.4 + x = -1.326649916 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + x = -1.326649916 + 4.4 x = -1.326649916 + 4.4 Combine like terms: -1.326649916 + 4.4 = 3.073350084 x = 3.073350084 Simplifying x = 3.073350084Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.726649916, 3.073350084}
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