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Simplifying 0 = x2 + 30x + 60 Reorder the terms: 0 = 60 + 30x + x2 Solving 0 = 60 + 30x + x2 Solving for variable 'x'. Combine like terms: 0 + -60 = -60 -60 + -30x + -1x2 = 60 + 30x + x2 + -60 + -30x + -1x2 Reorder the terms: -60 + -30x + -1x2 = 60 + -60 + 30x + -30x + x2 + -1x2 Combine like terms: 60 + -60 = 0 -60 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 -60 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 -60 + -30x + -1x2 = 0 + x2 + -1x2 -60 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + -30x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(60 + 30x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(60 + 30x + x2)' equal to zero and attempt to solve: Simplifying 60 + 30x + x2 = 0 Solving 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 = 165 225 + 30x + x2 = 165 Factor a perfect square on the left side: (x + 15)(x + 15) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + 15) equal to 12.845232579 and -12.845232579.Subproblem 1
x + 15 = 12.845232579 Simplifying x + 15 = 12.845232579 Reorder the terms: 15 + x = 12.845232579 Solving 15 + x = 12.845232579 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 = 12.845232579 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.845232579 + -15 x = 12.845232579 + -15 Combine like terms: 12.845232579 + -15 = -2.154767421 x = -2.154767421 Simplifying x = -2.154767421Subproblem 2
x + 15 = -12.845232579 Simplifying x + 15 = -12.845232579 Reorder the terms: 15 + x = -12.845232579 Solving 15 + x = -12.845232579 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 = -12.845232579 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.845232579 + -15 x = -12.845232579 + -15 Combine like terms: -12.845232579 + -15 = -27.845232579 x = -27.845232579 Simplifying x = -27.845232579Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.154767421, -27.845232579}Solution
x = {-2.154767421, -27.845232579}
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