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Simplifying 2x2 + -26x + 3 = 0 Reorder the terms: 3 + -26x + 2x2 = 0 Solving 3 + -26x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -13x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -13x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -13x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -13x + x2 = 0 + -1.5 -13x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -13x + x2 = -1.5 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 = -1.5 + 42.25 Reorder the terms: 42.25 + -13x + x2 = -1.5 + 42.25 Combine like terms: -1.5 + 42.25 = 40.75 42.25 + -13x + x2 = 40.75 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 40.75 Calculate the square root of the right side: 6.383572667 Break this problem into two subproblems by setting (x + -6.5) equal to 6.383572667 and -6.383572667.Subproblem 1
x + -6.5 = 6.383572667 Simplifying x + -6.5 = 6.383572667 Reorder the terms: -6.5 + x = 6.383572667 Solving -6.5 + x = 6.383572667 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 = 6.383572667 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 6.383572667 + 6.5 x = 6.383572667 + 6.5 Combine like terms: 6.383572667 + 6.5 = 12.883572667 x = 12.883572667 Simplifying x = 12.883572667Subproblem 2
x + -6.5 = -6.383572667 Simplifying x + -6.5 = -6.383572667 Reorder the terms: -6.5 + x = -6.383572667 Solving -6.5 + x = -6.383572667 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 = -6.383572667 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -6.383572667 + 6.5 x = -6.383572667 + 6.5 Combine like terms: -6.383572667 + 6.5 = 0.116427333 x = 0.116427333 Simplifying x = 0.116427333Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.883572667, 0.116427333}
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