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Simplifying 400 + -0.1x + -0.6x2 = 0 Solving 400 + -0.1x + -0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.6 the coefficient of the squared term: Divide each side by '-0.6'. -666.6666667 + 0.1666666667x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + 0.1666666667x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + 0.1666666667x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + 0.1666666667x + x2 = 0 + 666.6666667 0.1666666667x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 0.1666666667x + x2 = 666.6666667 The x term is 0.1666666667x. Take half its coefficient (0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. 0.1666666667x + 0.006944444447 + x2 = 666.6666667 + 0.006944444447 Reorder the terms: 0.006944444447 + 0.1666666667x + x2 = 666.6666667 + 0.006944444447 Combine like terms: 666.6666667 + 0.006944444447 = 666.673611144447 0.006944444447 + 0.1666666667x + x2 = 666.673611144447 Factor a perfect square on the left side: (x + 0.08333333335)(x + 0.08333333335) = 666.673611144447 Calculate the square root of the right side: 25.820023454 Break this problem into two subproblems by setting (x + 0.08333333335) equal to 25.820023454 and -25.820023454.Subproblem 1
x + 0.08333333335 = 25.820023454 Simplifying x + 0.08333333335 = 25.820023454 Reorder the terms: 0.08333333335 + x = 25.820023454 Solving 0.08333333335 + x = 25.820023454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = 25.820023454 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = 25.820023454 + -0.08333333335 x = 25.820023454 + -0.08333333335 Combine like terms: 25.820023454 + -0.08333333335 = 25.73669012065 x = 25.73669012065 Simplifying x = 25.73669012065Subproblem 2
x + 0.08333333335 = -25.820023454 Simplifying x + 0.08333333335 = -25.820023454 Reorder the terms: 0.08333333335 + x = -25.820023454 Solving 0.08333333335 + x = -25.820023454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08333333335' to each side of the equation. 0.08333333335 + -0.08333333335 + x = -25.820023454 + -0.08333333335 Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000 0.00000000000 + x = -25.820023454 + -0.08333333335 x = -25.820023454 + -0.08333333335 Combine like terms: -25.820023454 + -0.08333333335 = -25.90335678735 x = -25.90335678735 Simplifying x = -25.90335678735Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.73669012065, -25.90335678735}
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