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Simplifying x2 + 188x + 36 = -9 Reorder the terms: 36 + 188x + x2 = -9 Solving 36 + 188x + x2 = -9 Solving for variable 'x'. Reorder the terms: 36 + 9 + 188x + x2 = -9 + 9 Combine like terms: 36 + 9 = 45 45 + 188x + x2 = -9 + 9 Combine like terms: -9 + 9 = 0 45 + 188x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + 188x + -45 + x2 = 0 + -45 Reorder the terms: 45 + -45 + 188x + x2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 188x + x2 = 0 + -45 188x + x2 = 0 + -45 Combine like terms: 0 + -45 = -45 188x + x2 = -45 The x term is 188x. Take half its coefficient (94). Square it (8836) and add it to both sides. Add '8836' to each side of the equation. 188x + 8836 + x2 = -45 + 8836 Reorder the terms: 8836 + 188x + x2 = -45 + 8836 Combine like terms: -45 + 8836 = 8791 8836 + 188x + x2 = 8791 Factor a perfect square on the left side: (x + 94)(x + 94) = 8791 Calculate the square root of the right side: 93.760332764 Break this problem into two subproblems by setting (x + 94) equal to 93.760332764 and -93.760332764.Subproblem 1
x + 94 = 93.760332764 Simplifying x + 94 = 93.760332764 Reorder the terms: 94 + x = 93.760332764 Solving 94 + x = 93.760332764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-94' to each side of the equation. 94 + -94 + x = 93.760332764 + -94 Combine like terms: 94 + -94 = 0 0 + x = 93.760332764 + -94 x = 93.760332764 + -94 Combine like terms: 93.760332764 + -94 = -0.239667236 x = -0.239667236 Simplifying x = -0.239667236Subproblem 2
x + 94 = -93.760332764 Simplifying x + 94 = -93.760332764 Reorder the terms: 94 + x = -93.760332764 Solving 94 + x = -93.760332764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-94' to each side of the equation. 94 + -94 + x = -93.760332764 + -94 Combine like terms: 94 + -94 = 0 0 + x = -93.760332764 + -94 x = -93.760332764 + -94 Combine like terms: -93.760332764 + -94 = -187.760332764 x = -187.760332764 Simplifying x = -187.760332764Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.239667236, -187.760332764}
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