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Simplifying x2 + -28x + 23 = 0 Reorder the terms: 23 + -28x + x2 = 0 Solving 23 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-23' to each side of the equation. 23 + -28x + -23 + x2 = 0 + -23 Reorder the terms: 23 + -23 + -28x + x2 = 0 + -23 Combine like terms: 23 + -23 = 0 0 + -28x + x2 = 0 + -23 -28x + x2 = 0 + -23 Combine like terms: 0 + -23 = -23 -28x + x2 = -23 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 = -23 + 196 Reorder the terms: 196 + -28x + x2 = -23 + 196 Combine like terms: -23 + 196 = 173 196 + -28x + x2 = 173 Factor a perfect square on the left side: (x + -14)(x + -14) = 173 Calculate the square root of the right side: 13.152946438 Break this problem into two subproblems by setting (x + -14) equal to 13.152946438 and -13.152946438.Subproblem 1
x + -14 = 13.152946438 Simplifying x + -14 = 13.152946438 Reorder the terms: -14 + x = 13.152946438 Solving -14 + x = 13.152946438 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 = 13.152946438 + 14 Combine like terms: -14 + 14 = 0 0 + x = 13.152946438 + 14 x = 13.152946438 + 14 Combine like terms: 13.152946438 + 14 = 27.152946438 x = 27.152946438 Simplifying x = 27.152946438Subproblem 2
x + -14 = -13.152946438 Simplifying x + -14 = -13.152946438 Reorder the terms: -14 + x = -13.152946438 Solving -14 + x = -13.152946438 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 = -13.152946438 + 14 Combine like terms: -14 + 14 = 0 0 + x = -13.152946438 + 14 x = -13.152946438 + 14 Combine like terms: -13.152946438 + 14 = 0.847053562 x = 0.847053562 Simplifying x = 0.847053562Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.152946438, 0.847053562}
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