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Simplifying 0.5x2 + -13x + -0.6 = 0 Reorder the terms: -0.6 + -13x + 0.5x2 = 0 Solving -0.6 + -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'. -1.2 + -26x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -26x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -26x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -26x + x2 = 0 + 1.2 -26x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -26x + x2 = 1.2 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 = 1.2 + 169 Reorder the terms: 169 + -26x + x2 = 1.2 + 169 Combine like terms: 1.2 + 169 = 170.2 169 + -26x + x2 = 170.2 Factor a perfect square on the left side: (x + -13)(x + -13) = 170.2 Calculate the square root of the right side: 13.046072206 Break this problem into two subproblems by setting (x + -13) equal to 13.046072206 and -13.046072206.Subproblem 1
x + -13 = 13.046072206 Simplifying x + -13 = 13.046072206 Reorder the terms: -13 + x = 13.046072206 Solving -13 + x = 13.046072206 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 = 13.046072206 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.046072206 + 13 x = 13.046072206 + 13 Combine like terms: 13.046072206 + 13 = 26.046072206 x = 26.046072206 Simplifying x = 26.046072206Subproblem 2
x + -13 = -13.046072206 Simplifying x + -13 = -13.046072206 Reorder the terms: -13 + x = -13.046072206 Solving -13 + x = -13.046072206 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 = -13.046072206 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.046072206 + 13 x = -13.046072206 + 13 Combine like terms: -13.046072206 + 13 = -0.046072206 x = -0.046072206 Simplifying x = -0.046072206Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.046072206, -0.046072206}
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