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Simplifying 0.8x2 + -4x + -600 = 0 Reorder the terms: -600 + -4x + 0.8x2 = 0 Solving -600 + -4x + 0.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -750 + -5x + x2 = 0 Move the constant term to the right: Add '750' to each side of the equation. -750 + -5x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -5x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -5x + x2 = 0 + 750 -5x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -5x + x2 = 750 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 750 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 750 + 6.25 Combine like terms: 750 + 6.25 = 756.25 6.25 + -5x + x2 = 756.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 756.25 Calculate the square root of the right side: 27.5 Break this problem into two subproblems by setting (x + -2.5) equal to 27.5 and -27.5.Subproblem 1
x + -2.5 = 27.5 Simplifying x + -2.5 = 27.5 Reorder the terms: -2.5 + x = 27.5 Solving -2.5 + x = 27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 27.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 27.5 + 2.5 x = 27.5 + 2.5 Combine like terms: 27.5 + 2.5 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -2.5 = -27.5 Simplifying x + -2.5 = -27.5 Reorder the terms: -2.5 + x = -27.5 Solving -2.5 + x = -27.5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -27.5 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -27.5 + 2.5 x = -27.5 + 2.5 Combine like terms: -27.5 + 2.5 = -25 x = -25 Simplifying x = -25Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -25}
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