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Simplifying 0.2x2 + -1.75x + 1.2 = 0 Reorder the terms: 1.2 + -1.75x + 0.2x2 = 0 Solving 1.2 + -1.75x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 6 + -8.75x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8.75x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -8.75x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8.75x + x2 = 0 + -6 -8.75x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8.75x + x2 = -6 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = -6 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = -6 + 19.140625 Combine like terms: -6 + 19.140625 = 13.140625 19.140625 + -8.75x + x2 = 13.140625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 13.140625 Calculate the square root of the right side: 3.625 Break this problem into two subproblems by setting (x + -4.375) equal to 3.625 and -3.625.Subproblem 1
x + -4.375 = 3.625 Simplifying x + -4.375 = 3.625 Reorder the terms: -4.375 + x = 3.625 Solving -4.375 + x = 3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 3.625 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 3.625 + 4.375 x = 3.625 + 4.375 Combine like terms: 3.625 + 4.375 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -4.375 = -3.625 Simplifying x + -4.375 = -3.625 Reorder the terms: -4.375 + x = -3.625 Solving -4.375 + x = -3.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -3.625 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -3.625 + 4.375 x = -3.625 + 4.375 Combine like terms: -3.625 + 4.375 = 0.75 x = 0.75 Simplifying x = 0.75Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 0.75}
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