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Simplifying x2 + 8x = 144 Reorder the terms: 8x + x2 = 144 Solving 8x + x2 = 144 Solving for variable 'x'. Reorder the terms: -144 + 8x + x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -144 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + 8x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + 8x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + 8x + x2 = 0 + 144 8x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 8x + x2 = 144 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 144 + 16 Reorder the terms: 16 + 8x + x2 = 144 + 16 Combine like terms: 144 + 16 = 160 16 + 8x + x2 = 160 Factor a perfect square on the left side: (x + 4)(x + 4) = 160 Calculate the square root of the right side: 12.649110641 Break this problem into two subproblems by setting (x + 4) equal to 12.649110641 and -12.649110641.Subproblem 1
x + 4 = 12.649110641 Simplifying x + 4 = 12.649110641 Reorder the terms: 4 + x = 12.649110641 Solving 4 + x = 12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 12.649110641 + -4 Combine like terms: 4 + -4 = 0 0 + x = 12.649110641 + -4 x = 12.649110641 + -4 Combine like terms: 12.649110641 + -4 = 8.649110641 x = 8.649110641 Simplifying x = 8.649110641Subproblem 2
x + 4 = -12.649110641 Simplifying x + 4 = -12.649110641 Reorder the terms: 4 + x = -12.649110641 Solving 4 + x = -12.649110641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -12.649110641 + -4 Combine like terms: 4 + -4 = 0 0 + x = -12.649110641 + -4 x = -12.649110641 + -4 Combine like terms: -12.649110641 + -4 = -16.649110641 x = -16.649110641 Simplifying x = -16.649110641Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.649110641, -16.649110641}
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