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Simplifying 4x2 + 105x + 567 = 0 Reorder the terms: 567 + 105x + 4x2 = 0 Solving 567 + 105x + 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'. 141.75 + 26.25x + x2 = 0 Move the constant term to the right: Add '-141.75' to each side of the equation. 141.75 + 26.25x + -141.75 + x2 = 0 + -141.75 Reorder the terms: 141.75 + -141.75 + 26.25x + x2 = 0 + -141.75 Combine like terms: 141.75 + -141.75 = 0.00 0.00 + 26.25x + x2 = 0 + -141.75 26.25x + x2 = 0 + -141.75 Combine like terms: 0 + -141.75 = -141.75 26.25x + x2 = -141.75 The x term is 26.25x. Take half its coefficient (13.125). Square it (172.265625) and add it to both sides. Add '172.265625' to each side of the equation. 26.25x + 172.265625 + x2 = -141.75 + 172.265625 Reorder the terms: 172.265625 + 26.25x + x2 = -141.75 + 172.265625 Combine like terms: -141.75 + 172.265625 = 30.515625 172.265625 + 26.25x + x2 = 30.515625 Factor a perfect square on the left side: (x + 13.125)(x + 13.125) = 30.515625 Calculate the square root of the right side: 5.524094948 Break this problem into two subproblems by setting (x + 13.125) equal to 5.524094948 and -5.524094948.Subproblem 1
x + 13.125 = 5.524094948 Simplifying x + 13.125 = 5.524094948 Reorder the terms: 13.125 + x = 5.524094948 Solving 13.125 + x = 5.524094948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.125' to each side of the equation. 13.125 + -13.125 + x = 5.524094948 + -13.125 Combine like terms: 13.125 + -13.125 = 0.000 0.000 + x = 5.524094948 + -13.125 x = 5.524094948 + -13.125 Combine like terms: 5.524094948 + -13.125 = -7.600905052 x = -7.600905052 Simplifying x = -7.600905052Subproblem 2
x + 13.125 = -5.524094948 Simplifying x + 13.125 = -5.524094948 Reorder the terms: 13.125 + x = -5.524094948 Solving 13.125 + x = -5.524094948 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.125' to each side of the equation. 13.125 + -13.125 + x = -5.524094948 + -13.125 Combine like terms: 13.125 + -13.125 = 0.000 0.000 + x = -5.524094948 + -13.125 x = -5.524094948 + -13.125 Combine like terms: -5.524094948 + -13.125 = -18.649094948 x = -18.649094948 Simplifying x = -18.649094948Solution
The solution to the problem is based on the solutions from the subproblems. x = {-7.600905052, -18.649094948}
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