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Simplifying 400x + -5x2 + -6 = 0 Reorder the terms: -6 + 400x + -5x2 = 0 Solving -6 + 400x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.2 + -80x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -80x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -80x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -80x + x2 = 0 + -1.2 -80x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -80x + x2 = -1.2 The x term is -80x. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80x + 1600 + x2 = -1.2 + 1600 Reorder the terms: 1600 + -80x + x2 = -1.2 + 1600 Combine like terms: -1.2 + 1600 = 1598.8 1600 + -80x + x2 = 1598.8 Factor a perfect square on the left side: (x + -40)(x + -40) = 1598.8 Calculate the square root of the right side: 39.984997186 Break this problem into two subproblems by setting (x + -40) equal to 39.984997186 and -39.984997186.Subproblem 1
x + -40 = 39.984997186 Simplifying x + -40 = 39.984997186 Reorder the terms: -40 + x = 39.984997186 Solving -40 + x = 39.984997186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 39.984997186 + 40 Combine like terms: -40 + 40 = 0 0 + x = 39.984997186 + 40 x = 39.984997186 + 40 Combine like terms: 39.984997186 + 40 = 79.984997186 x = 79.984997186 Simplifying x = 79.984997186Subproblem 2
x + -40 = -39.984997186 Simplifying x + -40 = -39.984997186 Reorder the terms: -40 + x = -39.984997186 Solving -40 + x = -39.984997186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -39.984997186 + 40 Combine like terms: -40 + 40 = 0 0 + x = -39.984997186 + 40 x = -39.984997186 + 40 Combine like terms: -39.984997186 + 40 = 0.015002814 x = 0.015002814 Simplifying x = 0.015002814Solution
The solution to the problem is based on the solutions from the subproblems. x = {79.984997186, 0.015002814}
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