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Simplifying x2 + -28x + 64 = 0 Reorder the terms: 64 + -28x + x2 = 0 Solving 64 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-64' to each side of the equation. 64 + -28x + -64 + x2 = 0 + -64 Reorder the terms: 64 + -64 + -28x + x2 = 0 + -64 Combine like terms: 64 + -64 = 0 0 + -28x + x2 = 0 + -64 -28x + x2 = 0 + -64 Combine like terms: 0 + -64 = -64 -28x + x2 = -64 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 = -64 + 196 Reorder the terms: 196 + -28x + x2 = -64 + 196 Combine like terms: -64 + 196 = 132 196 + -28x + x2 = 132 Factor a perfect square on the left side: (x + -14)(x + -14) = 132 Calculate the square root of the right side: 11.489125293 Break this problem into two subproblems by setting (x + -14) equal to 11.489125293 and -11.489125293.Subproblem 1
x + -14 = 11.489125293 Simplifying x + -14 = 11.489125293 Reorder the terms: -14 + x = 11.489125293 Solving -14 + x = 11.489125293 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 = 11.489125293 + 14 Combine like terms: -14 + 14 = 0 0 + x = 11.489125293 + 14 x = 11.489125293 + 14 Combine like terms: 11.489125293 + 14 = 25.489125293 x = 25.489125293 Simplifying x = 25.489125293Subproblem 2
x + -14 = -11.489125293 Simplifying x + -14 = -11.489125293 Reorder the terms: -14 + x = -11.489125293 Solving -14 + x = -11.489125293 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 = -11.489125293 + 14 Combine like terms: -14 + 14 = 0 0 + x = -11.489125293 + 14 x = -11.489125293 + 14 Combine like terms: -11.489125293 + 14 = 2.510874707 x = 2.510874707 Simplifying x = 2.510874707Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.489125293, 2.510874707}
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