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Simplifying -0.5x2 + 13x + 13 = 0 Reorder the terms: 13 + 13x + -0.5x2 = 0 Solving 13 + 13x + -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'. -26 + -26x + x2 = 0 Move the constant term to the right: Add '26' to each side of the equation. -26 + -26x + 26 + x2 = 0 + 26 Reorder the terms: -26 + 26 + -26x + x2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -26x + x2 = 0 + 26 -26x + x2 = 0 + 26 Combine like terms: 0 + 26 = 26 -26x + x2 = 26 The x term is -26x. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26x + 169 + x2 = 26 + 169 Reorder the terms: 169 + -26x + x2 = 26 + 169 Combine like terms: 26 + 169 = 195 169 + -26x + x2 = 195 Factor a perfect square on the left side: (x + -13)(x + -13) = 195 Calculate the square root of the right side: 13.964240044 Break this problem into two subproblems by setting (x + -13) equal to 13.964240044 and -13.964240044.Subproblem 1
x + -13 = 13.964240044 Simplifying x + -13 = 13.964240044 Reorder the terms: -13 + x = 13.964240044 Solving -13 + x = 13.964240044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = 13.964240044 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.964240044 + 13 x = 13.964240044 + 13 Combine like terms: 13.964240044 + 13 = 26.964240044 x = 26.964240044 Simplifying x = 26.964240044Subproblem 2
x + -13 = -13.964240044 Simplifying x + -13 = -13.964240044 Reorder the terms: -13 + x = -13.964240044 Solving -13 + x = -13.964240044 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + x = -13.964240044 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.964240044 + 13 x = -13.964240044 + 13 Combine like terms: -13.964240044 + 13 = -0.964240044 x = -0.964240044 Simplifying x = -0.964240044Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.964240044, -0.964240044}
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