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Simplifying 4x2 + 47x + 136 = 0 Reorder the terms: 136 + 47x + 4x2 = 0 Solving 136 + 47x + 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'. 34 + 11.75x + x2 = 0 Move the constant term to the right: Add '-34' to each side of the equation. 34 + 11.75x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + 11.75x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + 11.75x + x2 = 0 + -34 11.75x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 11.75x + x2 = -34 The x term is 11.75x. Take half its coefficient (5.875). Square it (34.515625) and add it to both sides. Add '34.515625' to each side of the equation. 11.75x + 34.515625 + x2 = -34 + 34.515625 Reorder the terms: 34.515625 + 11.75x + x2 = -34 + 34.515625 Combine like terms: -34 + 34.515625 = 0.515625 34.515625 + 11.75x + x2 = 0.515625 Factor a perfect square on the left side: (x + 5.875)(x + 5.875) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (x + 5.875) equal to 0.718070331 and -0.718070331.Subproblem 1
x + 5.875 = 0.718070331 Simplifying x + 5.875 = 0.718070331 Reorder the terms: 5.875 + x = 0.718070331 Solving 5.875 + x = 0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = 0.718070331 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = 0.718070331 + -5.875 x = 0.718070331 + -5.875 Combine like terms: 0.718070331 + -5.875 = -5.156929669 x = -5.156929669 Simplifying x = -5.156929669Subproblem 2
x + 5.875 = -0.718070331 Simplifying x + 5.875 = -0.718070331 Reorder the terms: 5.875 + x = -0.718070331 Solving 5.875 + x = -0.718070331 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.875' to each side of the equation. 5.875 + -5.875 + x = -0.718070331 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + x = -0.718070331 + -5.875 x = -0.718070331 + -5.875 Combine like terms: -0.718070331 + -5.875 = -6.593070331 x = -6.593070331 Simplifying x = -6.593070331Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.156929669, -6.593070331}
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