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Simplifying 4x2 + -40x + -375 = 0 Reorder the terms: -375 + -40x + 4x2 = 0 Solving -375 + -40x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -93.75 + -10x + x2 = 0 Move the constant term to the right: Add '93.75' to each side of the equation. -93.75 + -10x + 93.75 + x2 = 0 + 93.75 Reorder the terms: -93.75 + 93.75 + -10x + x2 = 0 + 93.75 Combine like terms: -93.75 + 93.75 = 0.00 0.00 + -10x + x2 = 0 + 93.75 -10x + x2 = 0 + 93.75 Combine like terms: 0 + 93.75 = 93.75 -10x + x2 = 93.75 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = 93.75 + 25 Reorder the terms: 25 + -10x + x2 = 93.75 + 25 Combine like terms: 93.75 + 25 = 118.75 25 + -10x + x2 = 118.75 Factor a perfect square on the left side: (x + -5)(x + -5) = 118.75 Calculate the square root of the right side: 10.897247359 Break this problem into two subproblems by setting (x + -5) equal to 10.897247359 and -10.897247359.Subproblem 1
x + -5 = 10.897247359 Simplifying x + -5 = 10.897247359 Reorder the terms: -5 + x = 10.897247359 Solving -5 + x = 10.897247359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 10.897247359 + 5 Combine like terms: -5 + 5 = 0 0 + x = 10.897247359 + 5 x = 10.897247359 + 5 Combine like terms: 10.897247359 + 5 = 15.897247359 x = 15.897247359 Simplifying x = 15.897247359Subproblem 2
x + -5 = -10.897247359 Simplifying x + -5 = -10.897247359 Reorder the terms: -5 + x = -10.897247359 Solving -5 + x = -10.897247359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -10.897247359 + 5 Combine like terms: -5 + 5 = 0 0 + x = -10.897247359 + 5 x = -10.897247359 + 5 Combine like terms: -10.897247359 + 5 = -5.897247359 x = -5.897247359 Simplifying x = -5.897247359Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.897247359, -5.897247359}
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