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Simplifying x2 + 8x = 950 Reorder the terms: 8x + x2 = 950 Solving 8x + x2 = 950 Solving for variable 'x'. Reorder the terms: -950 + 8x + x2 = 950 + -950 Combine like terms: 950 + -950 = 0 -950 + 8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '950' to each side of the equation. -950 + 8x + 950 + x2 = 0 + 950 Reorder the terms: -950 + 950 + 8x + x2 = 0 + 950 Combine like terms: -950 + 950 = 0 0 + 8x + x2 = 0 + 950 8x + x2 = 0 + 950 Combine like terms: 0 + 950 = 950 8x + x2 = 950 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 = 950 + 16 Reorder the terms: 16 + 8x + x2 = 950 + 16 Combine like terms: 950 + 16 = 966 16 + 8x + x2 = 966 Factor a perfect square on the left side: (x + 4)(x + 4) = 966 Calculate the square root of the right side: 31.080540536 Break this problem into two subproblems by setting (x + 4) equal to 31.080540536 and -31.080540536.Subproblem 1
x + 4 = 31.080540536 Simplifying x + 4 = 31.080540536 Reorder the terms: 4 + x = 31.080540536 Solving 4 + x = 31.080540536 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 = 31.080540536 + -4 Combine like terms: 4 + -4 = 0 0 + x = 31.080540536 + -4 x = 31.080540536 + -4 Combine like terms: 31.080540536 + -4 = 27.080540536 x = 27.080540536 Simplifying x = 27.080540536Subproblem 2
x + 4 = -31.080540536 Simplifying x + 4 = -31.080540536 Reorder the terms: 4 + x = -31.080540536 Solving 4 + x = -31.080540536 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 = -31.080540536 + -4 Combine like terms: 4 + -4 = 0 0 + x = -31.080540536 + -4 x = -31.080540536 + -4 Combine like terms: -31.080540536 + -4 = -35.080540536 x = -35.080540536 Simplifying x = -35.080540536Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.080540536, -35.080540536}
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