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Simplifying 0.664x2 + -9.3376x + 18.72 = 0 Reorder the terms: 18.72 + -9.3376x + 0.664x2 = 0 Solving 18.72 + -9.3376x + 0.664x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.664 the coefficient of the squared term: Divide each side by '0.664'. 28.19277108 + -14.0626506x + x2 = 0 Move the constant term to the right: Add '-28.19277108' to each side of the equation. 28.19277108 + -14.0626506x + -28.19277108 + x2 = 0 + -28.19277108 Reorder the terms: 28.19277108 + -28.19277108 + -14.0626506x + x2 = 0 + -28.19277108 Combine like terms: 28.19277108 + -28.19277108 = 0.00000000 0.00000000 + -14.0626506x + x2 = 0 + -28.19277108 -14.0626506x + x2 = 0 + -28.19277108 Combine like terms: 0 + -28.19277108 = -28.19277108 -14.0626506x + x2 = -28.19277108 The x term is -14.0626506x. Take half its coefficient (-7.0313253). Square it (49.43953547) and add it to both sides. Add '49.43953547' to each side of the equation. -14.0626506x + 49.43953547 + x2 = -28.19277108 + 49.43953547 Reorder the terms: 49.43953547 + -14.0626506x + x2 = -28.19277108 + 49.43953547 Combine like terms: -28.19277108 + 49.43953547 = 21.24676439 49.43953547 + -14.0626506x + x2 = 21.24676439 Factor a perfect square on the left side: (x + -7.0313253)(x + -7.0313253) = 21.24676439 Calculate the square root of the right side: 4.609421264 Break this problem into two subproblems by setting (x + -7.0313253) equal to 4.609421264 and -4.609421264.Subproblem 1
x + -7.0313253 = 4.609421264 Simplifying x + -7.0313253 = 4.609421264 Reorder the terms: -7.0313253 + x = 4.609421264 Solving -7.0313253 + x = 4.609421264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.0313253' to each side of the equation. -7.0313253 + 7.0313253 + x = 4.609421264 + 7.0313253 Combine like terms: -7.0313253 + 7.0313253 = 0.0000000 0.0000000 + x = 4.609421264 + 7.0313253 x = 4.609421264 + 7.0313253 Combine like terms: 4.609421264 + 7.0313253 = 11.640746564 x = 11.640746564 Simplifying x = 11.640746564Subproblem 2
x + -7.0313253 = -4.609421264 Simplifying x + -7.0313253 = -4.609421264 Reorder the terms: -7.0313253 + x = -4.609421264 Solving -7.0313253 + x = -4.609421264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.0313253' to each side of the equation. -7.0313253 + 7.0313253 + x = -4.609421264 + 7.0313253 Combine like terms: -7.0313253 + 7.0313253 = 0.0000000 0.0000000 + x = -4.609421264 + 7.0313253 x = -4.609421264 + 7.0313253 Combine like terms: -4.609421264 + 7.0313253 = 2.421904036 x = 2.421904036 Simplifying x = 2.421904036Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.640746564, 2.421904036}
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