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Simplifying 2x2 + -4.8x = 1.2 Reorder the terms: -4.8x + 2x2 = 1.2 Solving -4.8x + 2x2 = 1.2 Solving for variable 'x'. Reorder the terms: -1.2 + -4.8x + 2x2 = 1.2 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 -1.2 + -4.8x + 2x2 = 0.0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.6 + -2.4x + x2 = 0.0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + -2.4x + 0.6 + x2 = 0.0 + 0.6 Reorder the terms: -0.6 + 0.6 + -2.4x + x2 = 0.0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + -2.4x + x2 = 0.0 + 0.6 -2.4x + x2 = 0.0 + 0.6 Combine like terms: 0.0 + 0.6 = 0.6 -2.4x + x2 = 0.6 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = 0.6 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 0.6 + 1.44 Combine like terms: 0.6 + 1.44 = 2.04 1.44 + -2.4x + x2 = 2.04 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 2.04 Calculate the square root of the right side: 1.428285686 Break this problem into two subproblems by setting (x + -1.2) equal to 1.428285686 and -1.428285686.Subproblem 1
x + -1.2 = 1.428285686 Simplifying x + -1.2 = 1.428285686 Reorder the terms: -1.2 + x = 1.428285686 Solving -1.2 + x = 1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 1.428285686 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.428285686 + 1.2 x = 1.428285686 + 1.2 Combine like terms: 1.428285686 + 1.2 = 2.628285686 x = 2.628285686 Simplifying x = 2.628285686Subproblem 2
x + -1.2 = -1.428285686 Simplifying x + -1.2 = -1.428285686 Reorder the terms: -1.2 + x = -1.428285686 Solving -1.2 + x = -1.428285686 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -1.428285686 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.428285686 + 1.2 x = -1.428285686 + 1.2 Combine like terms: -1.428285686 + 1.2 = -0.228285686 x = -0.228285686 Simplifying x = -0.228285686Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.628285686, -0.228285686}
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