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Simplifying x2 + 6x + -188 = 0 Reorder the terms: -188 + 6x + x2 = 0 Solving -188 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '188' to each side of the equation. -188 + 6x + 188 + x2 = 0 + 188 Reorder the terms: -188 + 188 + 6x + x2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + 6x + x2 = 0 + 188 6x + x2 = 0 + 188 Combine like terms: 0 + 188 = 188 6x + x2 = 188 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 188 + 9 Reorder the terms: 9 + 6x + x2 = 188 + 9 Combine like terms: 188 + 9 = 197 9 + 6x + x2 = 197 Factor a perfect square on the left side: (x + 3)(x + 3) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (x + 3) equal to 14.035668848 and -14.035668848.Subproblem 1
x + 3 = 14.035668848 Simplifying x + 3 = 14.035668848 Reorder the terms: 3 + x = 14.035668848 Solving 3 + x = 14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 14.035668848 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.035668848 + -3 x = 14.035668848 + -3 Combine like terms: 14.035668848 + -3 = 11.035668848 x = 11.035668848 Simplifying x = 11.035668848Subproblem 2
x + 3 = -14.035668848 Simplifying x + 3 = -14.035668848 Reorder the terms: 3 + x = -14.035668848 Solving 3 + x = -14.035668848 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -14.035668848 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.035668848 + -3 x = -14.035668848 + -3 Combine like terms: -14.035668848 + -3 = -17.035668848 x = -17.035668848 Simplifying x = -17.035668848Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.035668848, -17.035668848}
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