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Simplifying x2 + -60x + 190 = 0 Reorder the terms: 190 + -60x + x2 = 0 Solving 190 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-190' to each side of the equation. 190 + -60x + -190 + x2 = 0 + -190 Reorder the terms: 190 + -190 + -60x + x2 = 0 + -190 Combine like terms: 190 + -190 = 0 0 + -60x + x2 = 0 + -190 -60x + x2 = 0 + -190 Combine like terms: 0 + -190 = -190 -60x + x2 = -190 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -190 + 900 Reorder the terms: 900 + -60x + x2 = -190 + 900 Combine like terms: -190 + 900 = 710 900 + -60x + x2 = 710 Factor a perfect square on the left side: (x + -30)(x + -30) = 710 Calculate the square root of the right side: 26.645825189 Break this problem into two subproblems by setting (x + -30) equal to 26.645825189 and -26.645825189.Subproblem 1
x + -30 = 26.645825189 Simplifying x + -30 = 26.645825189 Reorder the terms: -30 + x = 26.645825189 Solving -30 + x = 26.645825189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 26.645825189 + 30 Combine like terms: -30 + 30 = 0 0 + x = 26.645825189 + 30 x = 26.645825189 + 30 Combine like terms: 26.645825189 + 30 = 56.645825189 x = 56.645825189 Simplifying x = 56.645825189Subproblem 2
x + -30 = -26.645825189 Simplifying x + -30 = -26.645825189 Reorder the terms: -30 + x = -26.645825189 Solving -30 + x = -26.645825189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -26.645825189 + 30 Combine like terms: -30 + 30 = 0 0 + x = -26.645825189 + 30 x = -26.645825189 + 30 Combine like terms: -26.645825189 + 30 = 3.354174811 x = 3.354174811 Simplifying x = 3.354174811Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.645825189, 3.354174811}
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