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Simplifying -4.8x2 + 1.8x + 2.2 = 0 Reorder the terms: 2.2 + 1.8x + -4.8x2 = 0 Solving 2.2 + 1.8x + -4.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.8 the coefficient of the squared term: Divide each side by '-4.8'. -0.4583333333 + -0.375x + x2 = 0 Move the constant term to the right: Add '0.4583333333' to each side of the equation. -0.4583333333 + -0.375x + 0.4583333333 + x2 = 0 + 0.4583333333 Reorder the terms: -0.4583333333 + 0.4583333333 + -0.375x + x2 = 0 + 0.4583333333 Combine like terms: -0.4583333333 + 0.4583333333 = 0.0000000000 0.0000000000 + -0.375x + x2 = 0 + 0.4583333333 -0.375x + x2 = 0 + 0.4583333333 Combine like terms: 0 + 0.4583333333 = 0.4583333333 -0.375x + x2 = 0.4583333333 The x term is -0.375x. Take half its coefficient (-0.1875). Square it (0.03515625) and add it to both sides. Add '0.03515625' to each side of the equation. -0.375x + 0.03515625 + x2 = 0.4583333333 + 0.03515625 Reorder the terms: 0.03515625 + -0.375x + x2 = 0.4583333333 + 0.03515625 Combine like terms: 0.4583333333 + 0.03515625 = 0.4934895833 0.03515625 + -0.375x + x2 = 0.4934895833 Factor a perfect square on the left side: (x + -0.1875)(x + -0.1875) = 0.4934895833 Calculate the square root of the right side: 0.702488137 Break this problem into two subproblems by setting (x + -0.1875) equal to 0.702488137 and -0.702488137.Subproblem 1
x + -0.1875 = 0.702488137 Simplifying x + -0.1875 = 0.702488137 Reorder the terms: -0.1875 + x = 0.702488137 Solving -0.1875 + x = 0.702488137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = 0.702488137 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = 0.702488137 + 0.1875 x = 0.702488137 + 0.1875 Combine like terms: 0.702488137 + 0.1875 = 0.889988137 x = 0.889988137 Simplifying x = 0.889988137Subproblem 2
x + -0.1875 = -0.702488137 Simplifying x + -0.1875 = -0.702488137 Reorder the terms: -0.1875 + x = -0.702488137 Solving -0.1875 + x = -0.702488137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1875' to each side of the equation. -0.1875 + 0.1875 + x = -0.702488137 + 0.1875 Combine like terms: -0.1875 + 0.1875 = 0.0000 0.0000 + x = -0.702488137 + 0.1875 x = -0.702488137 + 0.1875 Combine like terms: -0.702488137 + 0.1875 = -0.514988137 x = -0.514988137 Simplifying x = -0.514988137Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.889988137, -0.514988137}
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