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Simplifying -16 = x2 + 30x Reorder the terms: -16 = 30x + x2 Solving -16 = 30x + x2 Solving for variable 'x'. Reorder the terms: -16 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 -16 + -30x + -1x2 = 0 + x2 + -1x2 -16 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -16 + -30x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(16 + 30x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(16 + 30x + x2)' equal to zero and attempt to solve: Simplifying 16 + 30x + x2 = 0 Solving 16 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 30x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + 30x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 30x + x2 = 0 + -16 30x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 30x + x2 = -16 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 = -16 + 225 Reorder the terms: 225 + 30x + x2 = -16 + 225 Combine like terms: -16 + 225 = 209 225 + 30x + x2 = 209 Factor a perfect square on the left side: (x + 15)(x + 15) = 209 Calculate the square root of the right side: 14.456832295 Break this problem into two subproblems by setting (x + 15) equal to 14.456832295 and -14.456832295.Subproblem 1
x + 15 = 14.456832295 Simplifying x + 15 = 14.456832295 Reorder the terms: 15 + x = 14.456832295 Solving 15 + x = 14.456832295 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 = 14.456832295 + -15 Combine like terms: 15 + -15 = 0 0 + x = 14.456832295 + -15 x = 14.456832295 + -15 Combine like terms: 14.456832295 + -15 = -0.543167705 x = -0.543167705 Simplifying x = -0.543167705Subproblem 2
x + 15 = -14.456832295 Simplifying x + 15 = -14.456832295 Reorder the terms: 15 + x = -14.456832295 Solving 15 + x = -14.456832295 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 = -14.456832295 + -15 Combine like terms: 15 + -15 = 0 0 + x = -14.456832295 + -15 x = -14.456832295 + -15 Combine like terms: -14.456832295 + -15 = -29.456832295 x = -29.456832295 Simplifying x = -29.456832295Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.543167705, -29.456832295}Solution
x = {-0.543167705, -29.456832295}
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