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Simplifying -4.9x2 + 2.8x + 1.12 = 0 Reorder the terms: 1.12 + 2.8x + -4.9x2 = 0 Solving 1.12 + 2.8x + -4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.2285714286 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '0.2285714286' to each side of the equation. -0.2285714286 + -0.5714285714x + 0.2285714286 + x2 = 0 + 0.2285714286 Reorder the terms: -0.2285714286 + 0.2285714286 + -0.5714285714x + x2 = 0 + 0.2285714286 Combine like terms: -0.2285714286 + 0.2285714286 = 0.0000000000 0.0000000000 + -0.5714285714x + x2 = 0 + 0.2285714286 -0.5714285714x + x2 = 0 + 0.2285714286 Combine like terms: 0 + 0.2285714286 = 0.2285714286 -0.5714285714x + x2 = 0.2285714286 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 0.2285714286 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 0.2285714286 + 0.08163265305 Combine like terms: 0.2285714286 + 0.08163265305 = 0.31020408165 0.08163265305 + -0.5714285714x + x2 = 0.31020408165 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 0.31020408165 Calculate the square root of the right side: 0.556959677 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 0.556959677 and -0.556959677.Subproblem 1
x + -0.2857142857 = 0.556959677 Simplifying x + -0.2857142857 = 0.556959677 Reorder the terms: -0.2857142857 + x = 0.556959677 Solving -0.2857142857 + x = 0.556959677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 0.556959677 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 0.556959677 + 0.2857142857 x = 0.556959677 + 0.2857142857 Combine like terms: 0.556959677 + 0.2857142857 = 0.8426739627 x = 0.8426739627 Simplifying x = 0.8426739627Subproblem 2
x + -0.2857142857 = -0.556959677 Simplifying x + -0.2857142857 = -0.556959677 Reorder the terms: -0.2857142857 + x = -0.556959677 Solving -0.2857142857 + x = -0.556959677 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -0.556959677 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -0.556959677 + 0.2857142857 x = -0.556959677 + 0.2857142857 Combine like terms: -0.556959677 + 0.2857142857 = -0.2712453913 x = -0.2712453913 Simplifying x = -0.2712453913Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8426739627, -0.2712453913}
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