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Simplifying 0 = -0.004x2 + x + 2.5 Reorder the terms: 0 = 2.5 + x + -0.004x2 Solving 0 = 2.5 + x + -0.004x2 Solving for variable 'x'. Combine like terms: 0 + -2.5 = -2.5 -2.5 + -1x + 0.004x2 = 2.5 + x + -0.004x2 + -2.5 + -1x + 0.004x2 Reorder the terms: -2.5 + -1x + 0.004x2 = 2.5 + -2.5 + x + -1x + -0.004x2 + 0.004x2 Combine like terms: 2.5 + -2.5 = 0.0 -2.5 + -1x + 0.004x2 = 0.0 + x + -1x + -0.004x2 + 0.004x2 -2.5 + -1x + 0.004x2 = x + -1x + -0.004x2 + 0.004x2 Combine like terms: x + -1x = 0 -2.5 + -1x + 0.004x2 = 0 + -0.004x2 + 0.004x2 -2.5 + -1x + 0.004x2 = -0.004x2 + 0.004x2 Combine like terms: -0.004x2 + 0.004x2 = 0.000 -2.5 + -1x + 0.004x2 = 0.000 Begin completing the square. Divide all terms by 0.004 the coefficient of the squared term: Divide each side by '0.004'. -625 + -250x + x2 = 0 Move the constant term to the right: Add '625' to each side of the equation. -625 + -250x + 625 + x2 = 0 + 625 Reorder the terms: -625 + 625 + -250x + x2 = 0 + 625 Combine like terms: -625 + 625 = 0 0 + -250x + x2 = 0 + 625 -250x + x2 = 0 + 625 Combine like terms: 0 + 625 = 625 -250x + x2 = 625 The x term is -250x. Take half its coefficient (-125). Square it (15625) and add it to both sides. Add '15625' to each side of the equation. -250x + 15625 + x2 = 625 + 15625 Reorder the terms: 15625 + -250x + x2 = 625 + 15625 Combine like terms: 625 + 15625 = 16250 15625 + -250x + x2 = 16250 Factor a perfect square on the left side: (x + -125)(x + -125) = 16250 Calculate the square root of the right side: 127.47548784 Break this problem into two subproblems by setting (x + -125) equal to 127.47548784 and -127.47548784.Subproblem 1
x + -125 = 127.47548784 Simplifying x + -125 = 127.47548784 Reorder the terms: -125 + x = 127.47548784 Solving -125 + x = 127.47548784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 127.47548784 + 125 Combine like terms: -125 + 125 = 0 0 + x = 127.47548784 + 125 x = 127.47548784 + 125 Combine like terms: 127.47548784 + 125 = 252.47548784 x = 252.47548784 Simplifying x = 252.47548784Subproblem 2
x + -125 = -127.47548784 Simplifying x + -125 = -127.47548784 Reorder the terms: -125 + x = -127.47548784 Solving -125 + x = -127.47548784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -127.47548784 + 125 Combine like terms: -125 + 125 = 0 0 + x = -127.47548784 + 125 x = -127.47548784 + 125 Combine like terms: -127.47548784 + 125 = -2.47548784 x = -2.47548784 Simplifying x = -2.47548784Solution
The solution to the problem is based on the solutions from the subproblems. x = {252.47548784, -2.47548784}
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