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Simplifying 0 = x2 + -13x + -25 Reorder the terms: 0 = -25 + -13x + x2 Solving 0 = -25 + -13x + x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 13x + -1x2 = -25 + -13x + x2 + 25 + 13x + -1x2 Reorder the terms: 25 + 13x + -1x2 = -25 + 25 + -13x + 13x + x2 + -1x2 Combine like terms: -25 + 25 = 0 25 + 13x + -1x2 = 0 + -13x + 13x + x2 + -1x2 25 + 13x + -1x2 = -13x + 13x + x2 + -1x2 Combine like terms: -13x + 13x = 0 25 + 13x + -1x2 = 0 + x2 + -1x2 25 + 13x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + 13x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + -13x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -13x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + -13x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -13x + x2 = 0 + 25 -13x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 -13x + x2 = 25 The x term is -13x. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13x + 42.25 + x2 = 25 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 25 + 42.25 Combine like terms: 25 + 42.25 = 67.25 42.25 + -13x + x2 = 67.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 67.25 Calculate the square root of the right side: 8.200609733 Break this problem into two subproblems by setting (x + -6.5) equal to 8.200609733 and -8.200609733.Subproblem 1
x + -6.5 = 8.200609733 Simplifying x + -6.5 = 8.200609733 Reorder the terms: -6.5 + x = 8.200609733 Solving -6.5 + x = 8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = 8.200609733 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.200609733 + 6.5 x = 8.200609733 + 6.5 Combine like terms: 8.200609733 + 6.5 = 14.700609733 x = 14.700609733 Simplifying x = 14.700609733Subproblem 2
x + -6.5 = -8.200609733 Simplifying x + -6.5 = -8.200609733 Reorder the terms: -6.5 + x = -8.200609733 Solving -6.5 + x = -8.200609733 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + x = -8.200609733 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.200609733 + 6.5 x = -8.200609733 + 6.5 Combine like terms: -8.200609733 + 6.5 = -1.700609733 x = -1.700609733 Simplifying x = -1.700609733Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.700609733, -1.700609733}
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