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Simplifying x2 + -26x + -10.2 = 0 Reorder the terms: -10.2 + -26x + x2 = 0 Solving -10.2 + -26x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '10.2' to each side of the equation. -10.2 + -26x + 10.2 + x2 = 0 + 10.2 Reorder the terms: -10.2 + 10.2 + -26x + x2 = 0 + 10.2 Combine like terms: -10.2 + 10.2 = 0.0 0.0 + -26x + x2 = 0 + 10.2 -26x + x2 = 0 + 10.2 Combine like terms: 0 + 10.2 = 10.2 -26x + x2 = 10.2 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 = 10.2 + 169 Reorder the terms: 169 + -26x + x2 = 10.2 + 169 Combine like terms: 10.2 + 169 = 179.2 169 + -26x + x2 = 179.2 Factor a perfect square on the left side: (x + -13)(x + -13) = 179.2 Calculate the square root of the right side: 13.386560425 Break this problem into two subproblems by setting (x + -13) equal to 13.386560425 and -13.386560425.Subproblem 1
x + -13 = 13.386560425 Simplifying x + -13 = 13.386560425 Reorder the terms: -13 + x = 13.386560425 Solving -13 + x = 13.386560425 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 = 13.386560425 + 13 Combine like terms: -13 + 13 = 0 0 + x = 13.386560425 + 13 x = 13.386560425 + 13 Combine like terms: 13.386560425 + 13 = 26.386560425 x = 26.386560425 Simplifying x = 26.386560425Subproblem 2
x + -13 = -13.386560425 Simplifying x + -13 = -13.386560425 Reorder the terms: -13 + x = -13.386560425 Solving -13 + x = -13.386560425 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 = -13.386560425 + 13 Combine like terms: -13 + 13 = 0 0 + x = -13.386560425 + 13 x = -13.386560425 + 13 Combine like terms: -13.386560425 + 13 = -0.386560425 x = -0.386560425 Simplifying x = -0.386560425Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.386560425, -0.386560425}
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