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Simplifying x2 + -28x + 4 = 0 Reorder the terms: 4 + -28x + x2 = 0 Solving 4 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + -28x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -28x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -28x + x2 = 0 + -4 -28x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -28x + x2 = -4 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 = -4 + 196 Reorder the terms: 196 + -28x + x2 = -4 + 196 Combine like terms: -4 + 196 = 192 196 + -28x + x2 = 192 Factor a perfect square on the left side: (x + -14)(x + -14) = 192 Calculate the square root of the right side: 13.856406461 Break this problem into two subproblems by setting (x + -14) equal to 13.856406461 and -13.856406461.Subproblem 1
x + -14 = 13.856406461 Simplifying x + -14 = 13.856406461 Reorder the terms: -14 + x = 13.856406461 Solving -14 + x = 13.856406461 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 = 13.856406461 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.856406461 + 14 x = 13.856406461 + 14 Combine like terms: 13.856406461 + 14 = 27.856406461 x = 27.856406461 Simplifying x = 27.856406461Subproblem 2
x + -14 = -13.856406461 Simplifying x + -14 = -13.856406461 Reorder the terms: -14 + x = -13.856406461 Solving -14 + x = -13.856406461 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 = -13.856406461 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.856406461 + 14 x = -13.856406461 + 14 Combine like terms: -13.856406461 + 14 = 0.143593539 x = 0.143593539 Simplifying x = 0.143593539Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.856406461, 0.143593539}
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