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Simplifying 7x2 + 36x + 4 = 0 Reorder the terms: 4 + 36x + 7x2 = 0 Solving 4 + 36x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.5714285714 + 5.142857143x + x2 = 0 Move the constant term to the right: Add '-0.5714285714' to each side of the equation. 0.5714285714 + 5.142857143x + -0.5714285714 + x2 = 0 + -0.5714285714 Reorder the terms: 0.5714285714 + -0.5714285714 + 5.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0.5714285714 + -0.5714285714 = 0.0000000000 0.0000000000 + 5.142857143x + x2 = 0 + -0.5714285714 5.142857143x + x2 = 0 + -0.5714285714 Combine like terms: 0 + -0.5714285714 = -0.5714285714 5.142857143x + x2 = -0.5714285714 The x term is 5.142857143x. Take half its coefficient (2.571428572). Square it (6.612244901) and add it to both sides. Add '6.612244901' to each side of the equation. 5.142857143x + 6.612244901 + x2 = -0.5714285714 + 6.612244901 Reorder the terms: 6.612244901 + 5.142857143x + x2 = -0.5714285714 + 6.612244901 Combine like terms: -0.5714285714 + 6.612244901 = 6.0408163296 6.612244901 + 5.142857143x + x2 = 6.0408163296 Factor a perfect square on the left side: (x + 2.571428572)(x + 2.571428572) = 6.0408163296 Calculate the square root of the right side: 2.45780722 Break this problem into two subproblems by setting (x + 2.571428572) equal to 2.45780722 and -2.45780722.Subproblem 1
x + 2.571428572 = 2.45780722 Simplifying x + 2.571428572 = 2.45780722 Reorder the terms: 2.571428572 + x = 2.45780722 Solving 2.571428572 + x = 2.45780722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = 2.45780722 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = 2.45780722 + -2.571428572 x = 2.45780722 + -2.571428572 Combine like terms: 2.45780722 + -2.571428572 = -0.113621352 x = -0.113621352 Simplifying x = -0.113621352Subproblem 2
x + 2.571428572 = -2.45780722 Simplifying x + 2.571428572 = -2.45780722 Reorder the terms: 2.571428572 + x = -2.45780722 Solving 2.571428572 + x = -2.45780722 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.571428572' to each side of the equation. 2.571428572 + -2.571428572 + x = -2.45780722 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = -2.45780722 + -2.571428572 x = -2.45780722 + -2.571428572 Combine like terms: -2.45780722 + -2.571428572 = -5.029235792 x = -5.029235792 Simplifying x = -5.029235792Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.113621352, -5.029235792}
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