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Simplifying x2 + -32x + 196 = 0 Reorder the terms: 196 + -32x + x2 = 0 Solving 196 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-196' to each side of the equation. 196 + -32x + -196 + x2 = 0 + -196 Reorder the terms: 196 + -196 + -32x + x2 = 0 + -196 Combine like terms: 196 + -196 = 0 0 + -32x + x2 = 0 + -196 -32x + x2 = 0 + -196 Combine like terms: 0 + -196 = -196 -32x + x2 = -196 The x term is -32x. Take half its coefficient (-16). Square it (256) and add it to both sides. Add '256' to each side of the equation. -32x + 256 + x2 = -196 + 256 Reorder the terms: 256 + -32x + x2 = -196 + 256 Combine like terms: -196 + 256 = 60 256 + -32x + x2 = 60 Factor a perfect square on the left side: (x + -16)(x + -16) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -16) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -16 = 7.745966692 Simplifying x + -16 = 7.745966692 Reorder the terms: -16 + x = 7.745966692 Solving -16 + x = 7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = 7.745966692 + 16 Combine like terms: -16 + 16 = 0 0 + x = 7.745966692 + 16 x = 7.745966692 + 16 Combine like terms: 7.745966692 + 16 = 23.745966692 x = 23.745966692 Simplifying x = 23.745966692Subproblem 2
x + -16 = -7.745966692 Simplifying x + -16 = -7.745966692 Reorder the terms: -16 + x = -7.745966692 Solving -16 + x = -7.745966692 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16' to each side of the equation. -16 + 16 + x = -7.745966692 + 16 Combine like terms: -16 + 16 = 0 0 + x = -7.745966692 + 16 x = -7.745966692 + 16 Combine like terms: -7.745966692 + 16 = 8.254033308 x = 8.254033308 Simplifying x = 8.254033308Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.745966692, 8.254033308}
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