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Simplifying 0 = x2 + -16x + -188 Reorder the terms: 0 = -188 + -16x + x2 Solving 0 = -188 + -16x + x2 Solving for variable 'x'. Combine like terms: 0 + 188 = 188 188 + 16x + -1x2 = -188 + -16x + x2 + 188 + 16x + -1x2 Reorder the terms: 188 + 16x + -1x2 = -188 + 188 + -16x + 16x + x2 + -1x2 Combine like terms: -188 + 188 = 0 188 + 16x + -1x2 = 0 + -16x + 16x + x2 + -1x2 188 + 16x + -1x2 = -16x + 16x + x2 + -1x2 Combine like terms: -16x + 16x = 0 188 + 16x + -1x2 = 0 + x2 + -1x2 188 + 16x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 188 + 16x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -188 + -16x + x2 = 0 Move the constant term to the right: Add '188' to each side of the equation. -188 + -16x + 188 + x2 = 0 + 188 Reorder the terms: -188 + 188 + -16x + x2 = 0 + 188 Combine like terms: -188 + 188 = 0 0 + -16x + x2 = 0 + 188 -16x + x2 = 0 + 188 Combine like terms: 0 + 188 = 188 -16x + x2 = 188 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 188 + 64 Reorder the terms: 64 + -16x + x2 = 188 + 64 Combine like terms: 188 + 64 = 252 64 + -16x + x2 = 252 Factor a perfect square on the left side: (x + -8)(x + -8) = 252 Calculate the square root of the right side: 15.874507866 Break this problem into two subproblems by setting (x + -8) equal to 15.874507866 and -15.874507866.Subproblem 1
x + -8 = 15.874507866 Simplifying x + -8 = 15.874507866 Reorder the terms: -8 + x = 15.874507866 Solving -8 + x = 15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 15.874507866 + 8 Combine like terms: -8 + 8 = 0 0 + x = 15.874507866 + 8 x = 15.874507866 + 8 Combine like terms: 15.874507866 + 8 = 23.874507866 x = 23.874507866 Simplifying x = 23.874507866Subproblem 2
x + -8 = -15.874507866 Simplifying x + -8 = -15.874507866 Reorder the terms: -8 + x = -15.874507866 Solving -8 + x = -15.874507866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -15.874507866 + 8 Combine like terms: -8 + 8 = 0 0 + x = -15.874507866 + 8 x = -15.874507866 + 8 Combine like terms: -15.874507866 + 8 = -7.874507866 x = -7.874507866 Simplifying x = -7.874507866Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.874507866, -7.874507866}
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