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Simplifying 3x + 4 + 25 = 4x2 + 1 Reorder the terms: 4 + 25 + 3x = 4x2 + 1 Combine like terms: 4 + 25 = 29 29 + 3x = 4x2 + 1 Reorder the terms: 29 + 3x = 1 + 4x2 Solving 29 + 3x = 1 + 4x2 Solving for variable 'x'. Reorder the terms: 29 + -1 + 3x + -4x2 = 1 + 4x2 + -1 + -4x2 Combine like terms: 29 + -1 = 28 28 + 3x + -4x2 = 1 + 4x2 + -1 + -4x2 Reorder the terms: 28 + 3x + -4x2 = 1 + -1 + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 28 + 3x + -4x2 = 0 + 4x2 + -4x2 28 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 28 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7 + -0.75x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -0.75x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -0.75x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -0.75x + x2 = 0 + 7 -0.75x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -0.75x + x2 = 7 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 7 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 7 + 0.140625 Combine like terms: 7 + 0.140625 = 7.140625 0.140625 + -0.75x + x2 = 7.140625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -0.375) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -0.375 = 2.672194791 Simplifying x + -0.375 = 2.672194791 Reorder the terms: -0.375 + x = 2.672194791 Solving -0.375 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 2.672194791 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.672194791 + 0.375 x = 2.672194791 + 0.375 Combine like terms: 2.672194791 + 0.375 = 3.047194791 x = 3.047194791 Simplifying x = 3.047194791Subproblem 2
x + -0.375 = -2.672194791 Simplifying x + -0.375 = -2.672194791 Reorder the terms: -0.375 + x = -2.672194791 Solving -0.375 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -2.672194791 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.672194791 + 0.375 x = -2.672194791 + 0.375 Combine like terms: -2.672194791 + 0.375 = -2.297194791 x = -2.297194791 Simplifying x = -2.297194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.047194791, -2.297194791}
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