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Simplifying -0.5(x2) + 6x + 60 = 0 Reorder the terms: 60 + 6x + -0.5x2 = 0 Solving 60 + 6x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -120 + -12x + x2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + -12x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -12x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -12x + x2 = 0 + 120 -12x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -12x + x2 = 120 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 120 + 36 Reorder the terms: 36 + -12x + x2 = 120 + 36 Combine like terms: 120 + 36 = 156 36 + -12x + x2 = 156 Factor a perfect square on the left side: (x + -6)(x + -6) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -6) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -6 = 12.489995997 Simplifying x + -6 = 12.489995997 Reorder the terms: -6 + x = 12.489995997 Solving -6 + x = 12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 12.489995997 + 6 Combine like terms: -6 + 6 = 0 0 + x = 12.489995997 + 6 x = 12.489995997 + 6 Combine like terms: 12.489995997 + 6 = 18.489995997 x = 18.489995997 Simplifying x = 18.489995997Subproblem 2
x + -6 = -12.489995997 Simplifying x + -6 = -12.489995997 Reorder the terms: -6 + x = -12.489995997 Solving -6 + x = -12.489995997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -12.489995997 + 6 Combine like terms: -6 + 6 = 0 0 + x = -12.489995997 + 6 x = -12.489995997 + 6 Combine like terms: -12.489995997 + 6 = -6.489995997 x = -6.489995997 Simplifying x = -6.489995997Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.489995997, -6.489995997}
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