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Simplifying x2 + -28x + 28 = 0 Reorder the terms: 28 + -28x + x2 = 0 Solving 28 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -28x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -28x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -28x + x2 = 0 + -28 -28x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -28x + x2 = -28 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 = -28 + 196 Reorder the terms: 196 + -28x + x2 = -28 + 196 Combine like terms: -28 + 196 = 168 196 + -28x + x2 = 168 Factor a perfect square on the left side: (x + -14)(x + -14) = 168 Calculate the square root of the right side: 12.961481397 Break this problem into two subproblems by setting (x + -14) equal to 12.961481397 and -12.961481397.Subproblem 1
x + -14 = 12.961481397 Simplifying x + -14 = 12.961481397 Reorder the terms: -14 + x = 12.961481397 Solving -14 + x = 12.961481397 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 = 12.961481397 + 14 Combine like terms: -14 + 14 = 0 0 + x = 12.961481397 + 14 x = 12.961481397 + 14 Combine like terms: 12.961481397 + 14 = 26.961481397 x = 26.961481397 Simplifying x = 26.961481397Subproblem 2
x + -14 = -12.961481397 Simplifying x + -14 = -12.961481397 Reorder the terms: -14 + x = -12.961481397 Solving -14 + x = -12.961481397 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 = -12.961481397 + 14 Combine like terms: -14 + 14 = 0 0 + x = -12.961481397 + 14 x = -12.961481397 + 14 Combine like terms: -12.961481397 + 14 = 1.038518603 x = 1.038518603 Simplifying x = 1.038518603Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.961481397, 1.038518603}
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