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Simplifying -0.5x2 + 26x + 7 = 0 Reorder the terms: 7 + 26x + -0.5x2 = 0 Solving 7 + 26x + -0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -14 + -52x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -52x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -52x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -52x + x2 = 0 + 14 -52x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -52x + x2 = 14 The x term is -52x. Take half its coefficient (-26). Square it (676) and add it to both sides. Add '676' to each side of the equation. -52x + 676 + x2 = 14 + 676 Reorder the terms: 676 + -52x + x2 = 14 + 676 Combine like terms: 14 + 676 = 690 676 + -52x + x2 = 690 Factor a perfect square on the left side: (x + -26)(x + -26) = 690 Calculate the square root of the right side: 26.267851073 Break this problem into two subproblems by setting (x + -26) equal to 26.267851073 and -26.267851073.Subproblem 1
x + -26 = 26.267851073 Simplifying x + -26 = 26.267851073 Reorder the terms: -26 + x = 26.267851073 Solving -26 + x = 26.267851073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = 26.267851073 + 26 Combine like terms: -26 + 26 = 0 0 + x = 26.267851073 + 26 x = 26.267851073 + 26 Combine like terms: 26.267851073 + 26 = 52.267851073 x = 52.267851073 Simplifying x = 52.267851073Subproblem 2
x + -26 = -26.267851073 Simplifying x + -26 = -26.267851073 Reorder the terms: -26 + x = -26.267851073 Solving -26 + x = -26.267851073 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + x = -26.267851073 + 26 Combine like terms: -26 + 26 = 0 0 + x = -26.267851073 + 26 x = -26.267851073 + 26 Combine like terms: -26.267851073 + 26 = -0.267851073 x = -0.267851073 Simplifying x = -0.267851073Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.267851073, -0.267851073}
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