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Simplifying 1.25x2 + -10x + -17.2 = 0 Reorder the terms: -17.2 + -10x + 1.25x2 = 0 Solving -17.2 + -10x + 1.25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.25 the coefficient of the squared term: Divide each side by '1.25'. -13.76 + -8x + x2 = 0 Move the constant term to the right: Add '13.76' to each side of the equation. -13.76 + -8x + 13.76 + x2 = 0 + 13.76 Reorder the terms: -13.76 + 13.76 + -8x + x2 = 0 + 13.76 Combine like terms: -13.76 + 13.76 = 0.00 0.00 + -8x + x2 = 0 + 13.76 -8x + x2 = 0 + 13.76 Combine like terms: 0 + 13.76 = 13.76 -8x + x2 = 13.76 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 13.76 + 16 Reorder the terms: 16 + -8x + x2 = 13.76 + 16 Combine like terms: 13.76 + 16 = 29.76 16 + -8x + x2 = 29.76 Factor a perfect square on the left side: (x + -4)(x + -4) = 29.76 Calculate the square root of the right side: 5.455272679 Break this problem into two subproblems by setting (x + -4) equal to 5.455272679 and -5.455272679.Subproblem 1
x + -4 = 5.455272679 Simplifying x + -4 = 5.455272679 Reorder the terms: -4 + x = 5.455272679 Solving -4 + x = 5.455272679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 5.455272679 + 4 Combine like terms: -4 + 4 = 0 0 + x = 5.455272679 + 4 x = 5.455272679 + 4 Combine like terms: 5.455272679 + 4 = 9.455272679 x = 9.455272679 Simplifying x = 9.455272679Subproblem 2
x + -4 = -5.455272679 Simplifying x + -4 = -5.455272679 Reorder the terms: -4 + x = -5.455272679 Solving -4 + x = -5.455272679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -5.455272679 + 4 Combine like terms: -4 + 4 = 0 0 + x = -5.455272679 + 4 x = -5.455272679 + 4 Combine like terms: -5.455272679 + 4 = -1.455272679 x = -1.455272679 Simplifying x = -1.455272679Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.455272679, -1.455272679}
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