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Simplifying 7 = -0.4x(x + -10) Reorder the terms: 7 = -0.4x(-10 + x) 7 = (-10 * -0.4x + x * -0.4x) 7 = (4x + -0.4x2) Solving 7 = 4x + -0.4x2 Solving for variable 'x'. Reorder the terms: 7 + -4x + 0.4x2 = 4x + -4x + -0.4x2 + 0.4x2 Combine like terms: 4x + -4x = 0 7 + -4x + 0.4x2 = 0 + -0.4x2 + 0.4x2 7 + -4x + 0.4x2 = -0.4x2 + 0.4x2 Combine like terms: -0.4x2 + 0.4x2 = 0.0 7 + -4x + 0.4x2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. 17.5 + -10x + x2 = 0 Move the constant term to the right: Add '-17.5' to each side of the equation. 17.5 + -10x + -17.5 + x2 = 0 + -17.5 Reorder the terms: 17.5 + -17.5 + -10x + x2 = 0 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + -10x + x2 = 0 + -17.5 -10x + x2 = 0 + -17.5 Combine like terms: 0 + -17.5 = -17.5 -10x + x2 = -17.5 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 = -17.5 + 25 Reorder the terms: 25 + -10x + x2 = -17.5 + 25 Combine like terms: -17.5 + 25 = 7.5 25 + -10x + x2 = 7.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 7.5 Calculate the square root of the right side: 2.738612788 Break this problem into two subproblems by setting (x + -5) equal to 2.738612788 and -2.738612788.Subproblem 1
x + -5 = 2.738612788 Simplifying x + -5 = 2.738612788 Reorder the terms: -5 + x = 2.738612788 Solving -5 + x = 2.738612788 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 = 2.738612788 + 5 Combine like terms: -5 + 5 = 0 0 + x = 2.738612788 + 5 x = 2.738612788 + 5 Combine like terms: 2.738612788 + 5 = 7.738612788 x = 7.738612788 Simplifying x = 7.738612788Subproblem 2
x + -5 = -2.738612788 Simplifying x + -5 = -2.738612788 Reorder the terms: -5 + x = -2.738612788 Solving -5 + x = -2.738612788 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 = -2.738612788 + 5 Combine like terms: -5 + 5 = 0 0 + x = -2.738612788 + 5 x = -2.738612788 + 5 Combine like terms: -2.738612788 + 5 = 2.261387212 x = 2.261387212 Simplifying x = 2.261387212Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.738612788, 2.261387212}
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