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Simplifying x2 + -14.14x + -100 = 0 Reorder the terms: -100 + -14.14x + x2 = 0 Solving -100 + -14.14x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -14.14x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -14.14x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -14.14x + x2 = 0 + 100 -14.14x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -14.14x + x2 = 100 The x term is -14.14x. Take half its coefficient (-7.07). Square it (49.9849) and add it to both sides. Add '49.9849' to each side of the equation. -14.14x + 49.9849 + x2 = 100 + 49.9849 Reorder the terms: 49.9849 + -14.14x + x2 = 100 + 49.9849 Combine like terms: 100 + 49.9849 = 149.9849 49.9849 + -14.14x + x2 = 149.9849 Factor a perfect square on the left side: (x + -7.07)(x + -7.07) = 149.9849 Calculate the square root of the right side: 12.246832243 Break this problem into two subproblems by setting (x + -7.07) equal to 12.246832243 and -12.246832243.Subproblem 1
x + -7.07 = 12.246832243 Simplifying x + -7.07 = 12.246832243 Reorder the terms: -7.07 + x = 12.246832243 Solving -7.07 + x = 12.246832243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.07' to each side of the equation. -7.07 + 7.07 + x = 12.246832243 + 7.07 Combine like terms: -7.07 + 7.07 = 0.00 0.00 + x = 12.246832243 + 7.07 x = 12.246832243 + 7.07 Combine like terms: 12.246832243 + 7.07 = 19.316832243 x = 19.316832243 Simplifying x = 19.316832243Subproblem 2
x + -7.07 = -12.246832243 Simplifying x + -7.07 = -12.246832243 Reorder the terms: -7.07 + x = -12.246832243 Solving -7.07 + x = -12.246832243 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.07' to each side of the equation. -7.07 + 7.07 + x = -12.246832243 + 7.07 Combine like terms: -7.07 + 7.07 = 0.00 0.00 + x = -12.246832243 + 7.07 x = -12.246832243 + 7.07 Combine like terms: -12.246832243 + 7.07 = -5.176832243 x = -5.176832243 Simplifying x = -5.176832243Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.316832243, -5.176832243}
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