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Simplifying 0 = x2 + -5x + -40 Reorder the terms: 0 = -40 + -5x + x2 Solving 0 = -40 + -5x + x2 Solving for variable 'x'. Combine like terms: 0 + 40 = 40 40 + 5x + -1x2 = -40 + -5x + x2 + 40 + 5x + -1x2 Reorder the terms: 40 + 5x + -1x2 = -40 + 40 + -5x + 5x + x2 + -1x2 Combine like terms: -40 + 40 = 0 40 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2 40 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 40 + 5x + -1x2 = 0 + x2 + -1x2 40 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 40 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -40 + -5x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + -5x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -5x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -5x + x2 = 0 + 40 -5x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -5x + x2 = 40 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 40 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 40 + 6.25 Combine like terms: 40 + 6.25 = 46.25 6.25 + -5x + x2 = 46.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 46.25 Calculate the square root of the right side: 6.800735254 Break this problem into two subproblems by setting (x + -2.5) equal to 6.800735254 and -6.800735254.Subproblem 1
x + -2.5 = 6.800735254 Simplifying x + -2.5 = 6.800735254 Reorder the terms: -2.5 + x = 6.800735254 Solving -2.5 + x = 6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 6.800735254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 6.800735254 + 2.5 x = 6.800735254 + 2.5 Combine like terms: 6.800735254 + 2.5 = 9.300735254 x = 9.300735254 Simplifying x = 9.300735254Subproblem 2
x + -2.5 = -6.800735254 Simplifying x + -2.5 = -6.800735254 Reorder the terms: -2.5 + x = -6.800735254 Solving -2.5 + x = -6.800735254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -6.800735254 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -6.800735254 + 2.5 x = -6.800735254 + 2.5 Combine like terms: -6.800735254 + 2.5 = -4.300735254 x = -4.300735254 Simplifying x = -4.300735254Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.300735254, -4.300735254}
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