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Simplifying 0 = x2 + 30x + 37 Reorder the terms: 0 = 37 + 30x + x2 Solving 0 = 37 + 30x + x2 Solving for variable 'x'. Combine like terms: 0 + -37 = -37 -37 + -30x + -1x2 = 37 + 30x + x2 + -37 + -30x + -1x2 Reorder the terms: -37 + -30x + -1x2 = 37 + -37 + 30x + -30x + x2 + -1x2 Combine like terms: 37 + -37 = 0 -37 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 -37 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 -37 + -30x + -1x2 = 0 + x2 + -1x2 -37 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -37 + -30x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(37 + 30x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(37 + 30x + x2)' equal to zero and attempt to solve: Simplifying 37 + 30x + x2 = 0 Solving 37 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-37' to each side of the equation. 37 + 30x + -37 + x2 = 0 + -37 Reorder the terms: 37 + -37 + 30x + x2 = 0 + -37 Combine like terms: 37 + -37 = 0 0 + 30x + x2 = 0 + -37 30x + x2 = 0 + -37 Combine like terms: 0 + -37 = -37 30x + x2 = -37 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 = -37 + 225 Reorder the terms: 225 + 30x + x2 = -37 + 225 Combine like terms: -37 + 225 = 188 225 + 30x + x2 = 188 Factor a perfect square on the left side: (x + 15)(x + 15) = 188 Calculate the square root of the right side: 13.711309201 Break this problem into two subproblems by setting (x + 15) equal to 13.711309201 and -13.711309201.Subproblem 1
x + 15 = 13.711309201 Simplifying x + 15 = 13.711309201 Reorder the terms: 15 + x = 13.711309201 Solving 15 + x = 13.711309201 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 = 13.711309201 + -15 Combine like terms: 15 + -15 = 0 0 + x = 13.711309201 + -15 x = 13.711309201 + -15 Combine like terms: 13.711309201 + -15 = -1.288690799 x = -1.288690799 Simplifying x = -1.288690799Subproblem 2
x + 15 = -13.711309201 Simplifying x + 15 = -13.711309201 Reorder the terms: 15 + x = -13.711309201 Solving 15 + x = -13.711309201 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 = -13.711309201 + -15 Combine like terms: 15 + -15 = 0 0 + x = -13.711309201 + -15 x = -13.711309201 + -15 Combine like terms: -13.711309201 + -15 = -28.711309201 x = -28.711309201 Simplifying x = -28.711309201Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.288690799, -28.711309201}Solution
x = {-1.288690799, -28.711309201}
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