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Simplifying x2 + -28x + 170 = 0 Reorder the terms: 170 + -28x + x2 = 0 Solving 170 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-170' to each side of the equation. 170 + -28x + -170 + x2 = 0 + -170 Reorder the terms: 170 + -170 + -28x + x2 = 0 + -170 Combine like terms: 170 + -170 = 0 0 + -28x + x2 = 0 + -170 -28x + x2 = 0 + -170 Combine like terms: 0 + -170 = -170 -28x + x2 = -170 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -170 + 196 Reorder the terms: 196 + -28x + x2 = -170 + 196 Combine like terms: -170 + 196 = 26 196 + -28x + x2 = 26 Factor a perfect square on the left side: (x + -14)(x + -14) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + -14) equal to 5.099019514 and -5.099019514.Subproblem 1
x + -14 = 5.099019514 Simplifying x + -14 = 5.099019514 Reorder the terms: -14 + x = 5.099019514 Solving -14 + x = 5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 5.099019514 + 14 Combine like terms: -14 + 14 = 0 0 + x = 5.099019514 + 14 x = 5.099019514 + 14 Combine like terms: 5.099019514 + 14 = 19.099019514 x = 19.099019514 Simplifying x = 19.099019514Subproblem 2
x + -14 = -5.099019514 Simplifying x + -14 = -5.099019514 Reorder the terms: -14 + x = -5.099019514 Solving -14 + x = -5.099019514 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -5.099019514 + 14 Combine like terms: -14 + 14 = 0 0 + x = -5.099019514 + 14 x = -5.099019514 + 14 Combine like terms: -5.099019514 + 14 = 8.900980486 x = 8.900980486 Simplifying x = 8.900980486Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.099019514, 8.900980486}
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