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Simplifying 3.2x2 + 0.2x + -5 = 0 Reorder the terms: -5 + 0.2x + 3.2x2 = 0 Solving -5 + 0.2x + 3.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3.2 the coefficient of the squared term: Divide each side by '3.2'. -1.5625 + 0.0625x + x2 = 0 Move the constant term to the right: Add '1.5625' to each side of the equation. -1.5625 + 0.0625x + 1.5625 + x2 = 0 + 1.5625 Reorder the terms: -1.5625 + 1.5625 + 0.0625x + x2 = 0 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + 0.0625x + x2 = 0 + 1.5625 0.0625x + x2 = 0 + 1.5625 Combine like terms: 0 + 1.5625 = 1.5625 0.0625x + x2 = 1.5625 The x term is 0.0625x. Take half its coefficient (0.03125). Square it (0.0009765625) and add it to both sides. Add '0.0009765625' to each side of the equation. 0.0625x + 0.0009765625 + x2 = 1.5625 + 0.0009765625 Reorder the terms: 0.0009765625 + 0.0625x + x2 = 1.5625 + 0.0009765625 Combine like terms: 1.5625 + 0.0009765625 = 1.5634765625 0.0009765625 + 0.0625x + x2 = 1.5634765625 Factor a perfect square on the left side: (x + 0.03125)(x + 0.03125) = 1.5634765625 Calculate the square root of the right side: 1.250390564 Break this problem into two subproblems by setting (x + 0.03125) equal to 1.250390564 and -1.250390564.Subproblem 1
x + 0.03125 = 1.250390564 Simplifying x + 0.03125 = 1.250390564 Reorder the terms: 0.03125 + x = 1.250390564 Solving 0.03125 + x = 1.250390564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = 1.250390564 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = 1.250390564 + -0.03125 x = 1.250390564 + -0.03125 Combine like terms: 1.250390564 + -0.03125 = 1.219140564 x = 1.219140564 Simplifying x = 1.219140564Subproblem 2
x + 0.03125 = -1.250390564 Simplifying x + 0.03125 = -1.250390564 Reorder the terms: 0.03125 + x = -1.250390564 Solving 0.03125 + x = -1.250390564 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03125' to each side of the equation. 0.03125 + -0.03125 + x = -1.250390564 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + x = -1.250390564 + -0.03125 x = -1.250390564 + -0.03125 Combine like terms: -1.250390564 + -0.03125 = -1.281640564 x = -1.281640564 Simplifying x = -1.281640564Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.219140564, -1.281640564}
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