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Simplifying -5x2 + -37x + 18 = 0 Reorder the terms: 18 + -37x + -5x2 = 0 Solving 18 + -37x + -5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -3.6 + 7.4x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 7.4x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 7.4x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 7.4x + x2 = 0 + 3.6 7.4x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 7.4x + x2 = 3.6 The x term is 7.4x. Take half its coefficient (3.7). Square it (13.69) and add it to both sides. Add '13.69' to each side of the equation. 7.4x + 13.69 + x2 = 3.6 + 13.69 Reorder the terms: 13.69 + 7.4x + x2 = 3.6 + 13.69 Combine like terms: 3.6 + 13.69 = 17.29 13.69 + 7.4x + x2 = 17.29 Factor a perfect square on the left side: (x + 3.7)(x + 3.7) = 17.29 Calculate the square root of the right side: 4.158124577 Break this problem into two subproblems by setting (x + 3.7) equal to 4.158124577 and -4.158124577.Subproblem 1
x + 3.7 = 4.158124577 Simplifying x + 3.7 = 4.158124577 Reorder the terms: 3.7 + x = 4.158124577 Solving 3.7 + x = 4.158124577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = 4.158124577 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = 4.158124577 + -3.7 x = 4.158124577 + -3.7 Combine like terms: 4.158124577 + -3.7 = 0.458124577 x = 0.458124577 Simplifying x = 0.458124577Subproblem 2
x + 3.7 = -4.158124577 Simplifying x + 3.7 = -4.158124577 Reorder the terms: 3.7 + x = -4.158124577 Solving 3.7 + x = -4.158124577 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.7' to each side of the equation. 3.7 + -3.7 + x = -4.158124577 + -3.7 Combine like terms: 3.7 + -3.7 = 0.0 0.0 + x = -4.158124577 + -3.7 x = -4.158124577 + -3.7 Combine like terms: -4.158124577 + -3.7 = -7.858124577 x = -7.858124577 Simplifying x = -7.858124577Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.458124577, -7.858124577}
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