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Simplifying x2 + -32x + 246 = 0 Reorder the terms: 246 + -32x + x2 = 0 Solving 246 + -32x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-246' to each side of the equation. 246 + -32x + -246 + x2 = 0 + -246 Reorder the terms: 246 + -246 + -32x + x2 = 0 + -246 Combine like terms: 246 + -246 = 0 0 + -32x + x2 = 0 + -246 -32x + x2 = 0 + -246 Combine like terms: 0 + -246 = -246 -32x + x2 = -246 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 = -246 + 256 Reorder the terms: 256 + -32x + x2 = -246 + 256 Combine like terms: -246 + 256 = 10 256 + -32x + x2 = 10 Factor a perfect square on the left side: (x + -16)(x + -16) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (x + -16) equal to 3.16227766 and -3.16227766.Subproblem 1
x + -16 = 3.16227766 Simplifying x + -16 = 3.16227766 Reorder the terms: -16 + x = 3.16227766 Solving -16 + x = 3.16227766 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 = 3.16227766 + 16 Combine like terms: -16 + 16 = 0 0 + x = 3.16227766 + 16 x = 3.16227766 + 16 Combine like terms: 3.16227766 + 16 = 19.16227766 x = 19.16227766 Simplifying x = 19.16227766Subproblem 2
x + -16 = -3.16227766 Simplifying x + -16 = -3.16227766 Reorder the terms: -16 + x = -3.16227766 Solving -16 + x = -3.16227766 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 = -3.16227766 + 16 Combine like terms: -16 + 16 = 0 0 + x = -3.16227766 + 16 x = -3.16227766 + 16 Combine like terms: -3.16227766 + 16 = 12.83772234 x = 12.83772234 Simplifying x = 12.83772234Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.16227766, 12.83772234}
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