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Simplifying 1.12 = 2x2 + 5.6x Reorder the terms: 1.12 = 5.6x + 2x2 Solving 1.12 = 5.6x + 2x2 Solving for variable 'x'. Reorder the terms: 1.12 + -5.6x + -2x2 = 5.6x + -5.6x + 2x2 + -2x2 Combine like terms: 5.6x + -5.6x = 0.0 1.12 + -5.6x + -2x2 = 0.0 + 2x2 + -2x2 1.12 + -5.6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 1.12 + -5.6x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -0.56 + 2.8x + x2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + 2.8x + 0.56 + x2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + 2.8x + x2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + 2.8x + x2 = 0 + 0.56 2.8x + x2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 2.8x + x2 = 0.56 The x term is 2.8x. Take half its coefficient (1.4). Square it (1.96) and add it to both sides. Add '1.96' to each side of the equation. 2.8x + 1.96 + x2 = 0.56 + 1.96 Reorder the terms: 1.96 + 2.8x + x2 = 0.56 + 1.96 Combine like terms: 0.56 + 1.96 = 2.52 1.96 + 2.8x + x2 = 2.52 Factor a perfect square on the left side: (x + 1.4)(x + 1.4) = 2.52 Calculate the square root of the right side: 1.587450787 Break this problem into two subproblems by setting (x + 1.4) equal to 1.587450787 and -1.587450787.Subproblem 1
x + 1.4 = 1.587450787 Simplifying x + 1.4 = 1.587450787 Reorder the terms: 1.4 + x = 1.587450787 Solving 1.4 + x = 1.587450787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = 1.587450787 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = 1.587450787 + -1.4 x = 1.587450787 + -1.4 Combine like terms: 1.587450787 + -1.4 = 0.187450787 x = 0.187450787 Simplifying x = 0.187450787Subproblem 2
x + 1.4 = -1.587450787 Simplifying x + 1.4 = -1.587450787 Reorder the terms: 1.4 + x = -1.587450787 Solving 1.4 + x = -1.587450787 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.4' to each side of the equation. 1.4 + -1.4 + x = -1.587450787 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + x = -1.587450787 + -1.4 x = -1.587450787 + -1.4 Combine like terms: -1.587450787 + -1.4 = -2.987450787 x = -2.987450787 Simplifying x = -2.987450787Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.187450787, -2.987450787}
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