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Simplifying 2x2 + -4.8x = 3 Reorder the terms: -4.8x + 2x2 = 3 Solving -4.8x + 2x2 = 3 Solving for variable 'x'. Reorder the terms: -3 + -4.8x + 2x2 = 3 + -3 Combine like terms: 3 + -3 = 0 -3 + -4.8x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -2.4x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -2.4x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -2.4x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -2.4x + x2 = 0 + 1.5 -2.4x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -2.4x + x2 = 1.5 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 = 1.5 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = 1.5 + 1.44 Combine like terms: 1.5 + 1.44 = 2.94 1.44 + -2.4x + x2 = 2.94 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 2.94 Calculate the square root of the right side: 1.71464282 Break this problem into two subproblems by setting (x + -1.2) equal to 1.71464282 and -1.71464282.Subproblem 1
x + -1.2 = 1.71464282 Simplifying x + -1.2 = 1.71464282 Reorder the terms: -1.2 + x = 1.71464282 Solving -1.2 + x = 1.71464282 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 = 1.71464282 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 1.71464282 + 1.2 x = 1.71464282 + 1.2 Combine like terms: 1.71464282 + 1.2 = 2.91464282 x = 2.91464282 Simplifying x = 2.91464282Subproblem 2
x + -1.2 = -1.71464282 Simplifying x + -1.2 = -1.71464282 Reorder the terms: -1.2 + x = -1.71464282 Solving -1.2 + x = -1.71464282 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 = -1.71464282 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -1.71464282 + 1.2 x = -1.71464282 + 1.2 Combine like terms: -1.71464282 + 1.2 = -0.51464282 x = -0.51464282 Simplifying x = -0.51464282Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.91464282, -0.51464282}
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