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Simplifying 5x2 + -60x + 173 = 0 Reorder the terms: 173 + -60x + 5x2 = 0 Solving 173 + -60x + 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'. 34.6 + -12x + x2 = 0 Move the constant term to the right: Add '-34.6' to each side of the equation. 34.6 + -12x + -34.6 + x2 = 0 + -34.6 Reorder the terms: 34.6 + -34.6 + -12x + x2 = 0 + -34.6 Combine like terms: 34.6 + -34.6 = 0.0 0.0 + -12x + x2 = 0 + -34.6 -12x + x2 = 0 + -34.6 Combine like terms: 0 + -34.6 = -34.6 -12x + x2 = -34.6 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -34.6 + 36 Reorder the terms: 36 + -12x + x2 = -34.6 + 36 Combine like terms: -34.6 + 36 = 1.4 36 + -12x + x2 = 1.4 Factor a perfect square on the left side: (x + -6)(x + -6) = 1.4 Calculate the square root of the right side: 1.183215957 Break this problem into two subproblems by setting (x + -6) equal to 1.183215957 and -1.183215957.Subproblem 1
x + -6 = 1.183215957 Simplifying x + -6 = 1.183215957 Reorder the terms: -6 + x = 1.183215957 Solving -6 + x = 1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 1.183215957 + 6 Combine like terms: -6 + 6 = 0 0 + x = 1.183215957 + 6 x = 1.183215957 + 6 Combine like terms: 1.183215957 + 6 = 7.183215957 x = 7.183215957 Simplifying x = 7.183215957Subproblem 2
x + -6 = -1.183215957 Simplifying x + -6 = -1.183215957 Reorder the terms: -6 + x = -1.183215957 Solving -6 + x = -1.183215957 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -1.183215957 + 6 Combine like terms: -6 + 6 = 0 0 + x = -1.183215957 + 6 x = -1.183215957 + 6 Combine like terms: -1.183215957 + 6 = 4.816784043 x = 4.816784043 Simplifying x = 4.816784043Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.183215957, 4.816784043}
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