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Simplifying x2 + -10.5x + 1 = 0 Reorder the terms: 1 + -10.5x + x2 = 0 Solving 1 + -10.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -10.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -10.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -10.5x + x2 = 0 + -1 -10.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -10.5x + x2 = -1 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -1 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -1 + 27.5625 Combine like terms: -1 + 27.5625 = 26.5625 27.5625 + -10.5x + x2 = 26.5625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 26.5625 Calculate the square root of the right side: 5.153882032 Break this problem into two subproblems by setting (x + -5.25) equal to 5.153882032 and -5.153882032.Subproblem 1
x + -5.25 = 5.153882032 Simplifying x + -5.25 = 5.153882032 Reorder the terms: -5.25 + x = 5.153882032 Solving -5.25 + x = 5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 5.153882032 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 5.153882032 + 5.25 x = 5.153882032 + 5.25 Combine like terms: 5.153882032 + 5.25 = 10.403882032 x = 10.403882032 Simplifying x = 10.403882032Subproblem 2
x + -5.25 = -5.153882032 Simplifying x + -5.25 = -5.153882032 Reorder the terms: -5.25 + x = -5.153882032 Solving -5.25 + x = -5.153882032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -5.153882032 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -5.153882032 + 5.25 x = -5.153882032 + 5.25 Combine like terms: -5.153882032 + 5.25 = 0.096117968 x = 0.096117968 Simplifying x = 0.096117968Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.403882032, 0.096117968}
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