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Simplifying -0.6x2 + 30x + 150 = 0 Reorder the terms: 150 + 30x + -0.6x2 = 0 Solving 150 + 30x + -0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -250 + -50x + x2 = 0 Move the constant term to the right: Add '250' to each side of the equation. -250 + -50x + 250 + x2 = 0 + 250 Reorder the terms: -250 + 250 + -50x + x2 = 0 + 250 Combine like terms: -250 + 250 = 0 0 + -50x + x2 = 0 + 250 -50x + x2 = 0 + 250 Combine like terms: 0 + 250 = 250 -50x + x2 = 250 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = 250 + 625 Reorder the terms: 625 + -50x + x2 = 250 + 625 Combine like terms: 250 + 625 = 875 625 + -50x + x2 = 875 Factor a perfect square on the left side: (x + -25)(x + -25) = 875 Calculate the square root of the right side: 29.580398915 Break this problem into two subproblems by setting (x + -25) equal to 29.580398915 and -29.580398915.Subproblem 1
x + -25 = 29.580398915 Simplifying x + -25 = 29.580398915 Reorder the terms: -25 + x = 29.580398915 Solving -25 + x = 29.580398915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 29.580398915 + 25 Combine like terms: -25 + 25 = 0 0 + x = 29.580398915 + 25 x = 29.580398915 + 25 Combine like terms: 29.580398915 + 25 = 54.580398915 x = 54.580398915 Simplifying x = 54.580398915Subproblem 2
x + -25 = -29.580398915 Simplifying x + -25 = -29.580398915 Reorder the terms: -25 + x = -29.580398915 Solving -25 + x = -29.580398915 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -29.580398915 + 25 Combine like terms: -25 + 25 = 0 0 + x = -29.580398915 + 25 x = -29.580398915 + 25 Combine like terms: -29.580398915 + 25 = -4.580398915 x = -4.580398915 Simplifying x = -4.580398915Solution
The solution to the problem is based on the solutions from the subproblems. x = {54.580398915, -4.580398915}
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