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Simplifying x2 + -28x + 80 = 0 Reorder the terms: 80 + -28x + x2 = 0 Solving 80 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + -28x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + -28x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + -28x + x2 = 0 + -80 -28x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 -28x + x2 = -80 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 = -80 + 196 Reorder the terms: 196 + -28x + x2 = -80 + 196 Combine like terms: -80 + 196 = 116 196 + -28x + x2 = 116 Factor a perfect square on the left side: (x + -14)(x + -14) = 116 Calculate the square root of the right side: 10.770329614 Break this problem into two subproblems by setting (x + -14) equal to 10.770329614 and -10.770329614.Subproblem 1
x + -14 = 10.770329614 Simplifying x + -14 = 10.770329614 Reorder the terms: -14 + x = 10.770329614 Solving -14 + x = 10.770329614 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 = 10.770329614 + 14 Combine like terms: -14 + 14 = 0 0 + x = 10.770329614 + 14 x = 10.770329614 + 14 Combine like terms: 10.770329614 + 14 = 24.770329614 x = 24.770329614 Simplifying x = 24.770329614Subproblem 2
x + -14 = -10.770329614 Simplifying x + -14 = -10.770329614 Reorder the terms: -14 + x = -10.770329614 Solving -14 + x = -10.770329614 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 = -10.770329614 + 14 Combine like terms: -14 + 14 = 0 0 + x = -10.770329614 + 14 x = -10.770329614 + 14 Combine like terms: -10.770329614 + 14 = 3.229670386 x = 3.229670386 Simplifying x = 3.229670386Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.770329614, 3.229670386}
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