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Simplifying 4x2 + -35x + 28 = 0 Reorder the terms: 28 + -35x + 4x2 = 0 Solving 28 + -35x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + -8.75x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -8.75x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -8.75x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8.75x + x2 = 0 + -7 -8.75x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -8.75x + x2 = -7 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = -7 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = -7 + 19.140625 Combine like terms: -7 + 19.140625 = 12.140625 19.140625 + -8.75x + x2 = 12.140625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 12.140625 Calculate the square root of the right side: 3.484339966 Break this problem into two subproblems by setting (x + -4.375) equal to 3.484339966 and -3.484339966.Subproblem 1
x + -4.375 = 3.484339966 Simplifying x + -4.375 = 3.484339966 Reorder the terms: -4.375 + x = 3.484339966 Solving -4.375 + x = 3.484339966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 3.484339966 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 3.484339966 + 4.375 x = 3.484339966 + 4.375 Combine like terms: 3.484339966 + 4.375 = 7.859339966 x = 7.859339966 Simplifying x = 7.859339966Subproblem 2
x + -4.375 = -3.484339966 Simplifying x + -4.375 = -3.484339966 Reorder the terms: -4.375 + x = -3.484339966 Solving -4.375 + x = -3.484339966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -3.484339966 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -3.484339966 + 4.375 x = -3.484339966 + 4.375 Combine like terms: -3.484339966 + 4.375 = 0.890660034 x = 0.890660034 Simplifying x = 0.890660034Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.859339966, 0.890660034}
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