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Simplifying x2 + -28x + 40 = 0 Reorder the terms: 40 + -28x + x2 = 0 Solving 40 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -28x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -28x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -28x + x2 = 0 + -40 -28x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -28x + x2 = -40 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 = -40 + 196 Reorder the terms: 196 + -28x + x2 = -40 + 196 Combine like terms: -40 + 196 = 156 196 + -28x + x2 = 156 Factor a perfect square on the left side: (x + -14)(x + -14) = 156 Calculate the square root of the right side: 12.489995997 Break this problem into two subproblems by setting (x + -14) equal to 12.489995997 and -12.489995997.Subproblem 1
x + -14 = 12.489995997 Simplifying x + -14 = 12.489995997 Reorder the terms: -14 + x = 12.489995997 Solving -14 + x = 12.489995997 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 = 12.489995997 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.489995997 + 14 x = 12.489995997 + 14 Combine like terms: 12.489995997 + 14 = 26.489995997 x = 26.489995997 Simplifying x = 26.489995997Subproblem 2
x + -14 = -12.489995997 Simplifying x + -14 = -12.489995997 Reorder the terms: -14 + x = -12.489995997 Solving -14 + x = -12.489995997 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 = -12.489995997 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.489995997 + 14 x = -12.489995997 + 14 Combine like terms: -12.489995997 + 14 = 1.510004003 x = 1.510004003 Simplifying x = 1.510004003Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.489995997, 1.510004003}
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