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Simplifying 0.8x(x + -100) = 450 Reorder the terms: 0.8x(-100 + x) = 450 (-100 * 0.8x + x * 0.8x) = 450 (-80x + 0.8x2) = 450 Solving -80x + 0.8x2 = 450 Solving for variable 'x'. Reorder the terms: -450 + -80x + 0.8x2 = 450 + -450 Combine like terms: 450 + -450 = 0 -450 + -80x + 0.8x2 = 0 Begin completing the square. Divide all terms by 0.8 the coefficient of the squared term: Divide each side by '0.8'. -562.5 + -100x + x2 = 0 Move the constant term to the right: Add '562.5' to each side of the equation. -562.5 + -100x + 562.5 + x2 = 0 + 562.5 Reorder the terms: -562.5 + 562.5 + -100x + x2 = 0 + 562.5 Combine like terms: -562.5 + 562.5 = 0.0 0.0 + -100x + x2 = 0 + 562.5 -100x + x2 = 0 + 562.5 Combine like terms: 0 + 562.5 = 562.5 -100x + x2 = 562.5 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = 562.5 + 2500 Reorder the terms: 2500 + -100x + x2 = 562.5 + 2500 Combine like terms: 562.5 + 2500 = 3062.5 2500 + -100x + x2 = 3062.5 Factor a perfect square on the left side: (x + -50)(x + -50) = 3062.5 Calculate the square root of the right side: 55.339859053 Break this problem into two subproblems by setting (x + -50) equal to 55.339859053 and -55.339859053.Subproblem 1
x + -50 = 55.339859053 Simplifying x + -50 = 55.339859053 Reorder the terms: -50 + x = 55.339859053 Solving -50 + x = 55.339859053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 55.339859053 + 50 Combine like terms: -50 + 50 = 0 0 + x = 55.339859053 + 50 x = 55.339859053 + 50 Combine like terms: 55.339859053 + 50 = 105.339859053 x = 105.339859053 Simplifying x = 105.339859053Subproblem 2
x + -50 = -55.339859053 Simplifying x + -50 = -55.339859053 Reorder the terms: -50 + x = -55.339859053 Solving -50 + x = -55.339859053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -55.339859053 + 50 Combine like terms: -50 + 50 = 0 0 + x = -55.339859053 + 50 x = -55.339859053 + 50 Combine like terms: -55.339859053 + 50 = -5.339859053 x = -5.339859053 Simplifying x = -5.339859053Solution
The solution to the problem is based on the solutions from the subproblems. x = {105.339859053, -5.339859053}
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