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Simplifying -1.50x2 + 84x + -450 = 0 Reorder the terms: -450 + 84x + -1.50x2 = 0 Solving -450 + 84x + -1.50x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.50 the coefficient of the squared term: Divide each side by '-1.50'. 300 + -56x + x2 = 0 Move the constant term to the right: Add '-300' to each side of the equation. 300 + -56x + -300 + x2 = 0 + -300 Reorder the terms: 300 + -300 + -56x + x2 = 0 + -300 Combine like terms: 300 + -300 = 0 0 + -56x + x2 = 0 + -300 -56x + x2 = 0 + -300 Combine like terms: 0 + -300 = -300 -56x + x2 = -300 The x term is -56x. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56x + 784 + x2 = -300 + 784 Reorder the terms: 784 + -56x + x2 = -300 + 784 Combine like terms: -300 + 784 = 484 784 + -56x + x2 = 484 Factor a perfect square on the left side: (x + -28)(x + -28) = 484 Calculate the square root of the right side: 22 Break this problem into two subproblems by setting (x + -28) equal to 22 and -22.Subproblem 1
x + -28 = 22 Simplifying x + -28 = 22 Reorder the terms: -28 + x = 22 Solving -28 + x = 22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = 22 + 28 Combine like terms: -28 + 28 = 0 0 + x = 22 + 28 x = 22 + 28 Combine like terms: 22 + 28 = 50 x = 50 Simplifying x = 50Subproblem 2
x + -28 = -22 Simplifying x + -28 = -22 Reorder the terms: -28 + x = -22 Solving -28 + x = -22 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + x = -22 + 28 Combine like terms: -28 + 28 = 0 0 + x = -22 + 28 x = -22 + 28 Combine like terms: -22 + 28 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, 6}
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