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Simplifying 7x2 + 36x + -9 = 0 Reorder the terms: -9 + 36x + 7x2 = 0 Solving -9 + 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'. -1.285714286 + 5.142857143x + x2 = 0 Move the constant term to the right: Add '1.285714286' to each side of the equation. -1.285714286 + 5.142857143x + 1.285714286 + x2 = 0 + 1.285714286 Reorder the terms: -1.285714286 + 1.285714286 + 5.142857143x + x2 = 0 + 1.285714286 Combine like terms: -1.285714286 + 1.285714286 = 0.000000000 0.000000000 + 5.142857143x + x2 = 0 + 1.285714286 5.142857143x + x2 = 0 + 1.285714286 Combine like terms: 0 + 1.285714286 = 1.285714286 5.142857143x + x2 = 1.285714286 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 = 1.285714286 + 6.612244901 Reorder the terms: 6.612244901 + 5.142857143x + x2 = 1.285714286 + 6.612244901 Combine like terms: 1.285714286 + 6.612244901 = 7.897959187 6.612244901 + 5.142857143x + x2 = 7.897959187 Factor a perfect square on the left side: (x + 2.571428572)(x + 2.571428572) = 7.897959187 Calculate the square root of the right side: 2.810330797 Break this problem into two subproblems by setting (x + 2.571428572) equal to 2.810330797 and -2.810330797.Subproblem 1
x + 2.571428572 = 2.810330797 Simplifying x + 2.571428572 = 2.810330797 Reorder the terms: 2.571428572 + x = 2.810330797 Solving 2.571428572 + x = 2.810330797 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 = 2.810330797 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = 2.810330797 + -2.571428572 x = 2.810330797 + -2.571428572 Combine like terms: 2.810330797 + -2.571428572 = 0.238902225 x = 0.238902225 Simplifying x = 0.238902225Subproblem 2
x + 2.571428572 = -2.810330797 Simplifying x + 2.571428572 = -2.810330797 Reorder the terms: 2.571428572 + x = -2.810330797 Solving 2.571428572 + x = -2.810330797 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 = -2.810330797 + -2.571428572 Combine like terms: 2.571428572 + -2.571428572 = 0.000000000 0.000000000 + x = -2.810330797 + -2.571428572 x = -2.810330797 + -2.571428572 Combine like terms: -2.810330797 + -2.571428572 = -5.381759369 x = -5.381759369 Simplifying x = -5.381759369Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.238902225, -5.381759369}
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