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Simplifying X2 + 30X + -50 = 10 Reorder the terms: -50 + 30X + X2 = 10 Solving -50 + 30X + X2 = 10 Solving for variable 'X'. Reorder the terms: -50 + -10 + 30X + X2 = 10 + -10 Combine like terms: -50 + -10 = -60 -60 + 30X + X2 = 10 + -10 Combine like terms: 10 + -10 = 0 -60 + 30X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 30X + 60 + X2 = 0 + 60 Reorder the terms: -60 + 60 + 30X + X2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 30X + X2 = 0 + 60 30X + X2 = 0 + 60 Combine like terms: 0 + 60 = 60 30X + X2 = 60 The X term is 30X. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30X + 225 + X2 = 60 + 225 Reorder the terms: 225 + 30X + X2 = 60 + 225 Combine like terms: 60 + 225 = 285 225 + 30X + X2 = 285 Factor a perfect square on the left side: (X + 15)(X + 15) = 285 Calculate the square root of the right side: 16.881943016 Break this problem into two subproblems by setting (X + 15) equal to 16.881943016 and -16.881943016.Subproblem 1
X + 15 = 16.881943016 Simplifying X + 15 = 16.881943016 Reorder the terms: 15 + X = 16.881943016 Solving 15 + X = 16.881943016 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + X = 16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + X = 16.881943016 + -15 X = 16.881943016 + -15 Combine like terms: 16.881943016 + -15 = 1.881943016 X = 1.881943016 Simplifying X = 1.881943016Subproblem 2
X + 15 = -16.881943016 Simplifying X + 15 = -16.881943016 Reorder the terms: 15 + X = -16.881943016 Solving 15 + X = -16.881943016 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + X = -16.881943016 + -15 Combine like terms: 15 + -15 = 0 0 + X = -16.881943016 + -15 X = -16.881943016 + -15 Combine like terms: -16.881943016 + -15 = -31.881943016 X = -31.881943016 Simplifying X = -31.881943016Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.881943016, -31.881943016}
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