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Simplifying 1.5x2 + -30x + -504 = 0 Reorder the terms: -504 + -30x + 1.5x2 = 0 Solving -504 + -30x + 1.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. -336 + -20x + x2 = 0 Move the constant term to the right: Add '336' to each side of the equation. -336 + -20x + 336 + x2 = 0 + 336 Reorder the terms: -336 + 336 + -20x + x2 = 0 + 336 Combine like terms: -336 + 336 = 0 0 + -20x + x2 = 0 + 336 -20x + x2 = 0 + 336 Combine like terms: 0 + 336 = 336 -20x + x2 = 336 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 336 + 100 Reorder the terms: 100 + -20x + x2 = 336 + 100 Combine like terms: 336 + 100 = 436 100 + -20x + x2 = 436 Factor a perfect square on the left side: (x + -10)(x + -10) = 436 Calculate the square root of the right side: 20.880613018 Break this problem into two subproblems by setting (x + -10) equal to 20.880613018 and -20.880613018.Subproblem 1
x + -10 = 20.880613018 Simplifying x + -10 = 20.880613018 Reorder the terms: -10 + x = 20.880613018 Solving -10 + x = 20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 20.880613018 + 10 Combine like terms: -10 + 10 = 0 0 + x = 20.880613018 + 10 x = 20.880613018 + 10 Combine like terms: 20.880613018 + 10 = 30.880613018 x = 30.880613018 Simplifying x = 30.880613018Subproblem 2
x + -10 = -20.880613018 Simplifying x + -10 = -20.880613018 Reorder the terms: -10 + x = -20.880613018 Solving -10 + x = -20.880613018 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -20.880613018 + 10 Combine like terms: -10 + 10 = 0 0 + x = -20.880613018 + 10 x = -20.880613018 + 10 Combine like terms: -20.880613018 + 10 = -10.880613018 x = -10.880613018 Simplifying x = -10.880613018Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.880613018, -10.880613018}
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