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Simplifying (x2) + -1(64x) + (720) = 0 x2 + -1(64x) + (720) = 0 Remove parenthesis around (64x) x2 + -1 * 64x + (720) = 0 Multiply -1 * 64 x2 + -64x + (720) = 0 x2 + -64x + 720 = 0 Reorder the terms: 720 + -64x + x2 = 0 Solving 720 + -64x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-720' to each side of the equation. 720 + -64x + -720 + x2 = 0 + -720 Reorder the terms: 720 + -720 + -64x + x2 = 0 + -720 Combine like terms: 720 + -720 = 0 0 + -64x + x2 = 0 + -720 -64x + x2 = 0 + -720 Combine like terms: 0 + -720 = -720 -64x + x2 = -720 The x term is -64x. Take half its coefficient (-32). Square it (1024) and add it to both sides. Add '1024' to each side of the equation. -64x + 1024 + x2 = -720 + 1024 Reorder the terms: 1024 + -64x + x2 = -720 + 1024 Combine like terms: -720 + 1024 = 304 1024 + -64x + x2 = 304 Factor a perfect square on the left side: (x + -32)(x + -32) = 304 Calculate the square root of the right side: 17.435595774 Break this problem into two subproblems by setting (x + -32) equal to 17.435595774 and -17.435595774.Subproblem 1
x + -32 = 17.435595774 Simplifying x + -32 = 17.435595774 Reorder the terms: -32 + x = 17.435595774 Solving -32 + x = 17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = 17.435595774 + 32 Combine like terms: -32 + 32 = 0 0 + x = 17.435595774 + 32 x = 17.435595774 + 32 Combine like terms: 17.435595774 + 32 = 49.435595774 x = 49.435595774 Simplifying x = 49.435595774Subproblem 2
x + -32 = -17.435595774 Simplifying x + -32 = -17.435595774 Reorder the terms: -32 + x = -17.435595774 Solving -32 + x = -17.435595774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '32' to each side of the equation. -32 + 32 + x = -17.435595774 + 32 Combine like terms: -32 + 32 = 0 0 + x = -17.435595774 + 32 x = -17.435595774 + 32 Combine like terms: -17.435595774 + 32 = 14.564404226 x = 14.564404226 Simplifying x = 14.564404226Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.435595774, 14.564404226}
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