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Simplifying x2 + -60x + 30 = 0 Reorder the terms: 30 + -60x + x2 = 0 Solving 30 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -60x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -60x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -60x + x2 = 0 + -30 -60x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -60x + x2 = -30 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 = -30 + 900 Reorder the terms: 900 + -60x + x2 = -30 + 900 Combine like terms: -30 + 900 = 870 900 + -60x + x2 = 870 Factor a perfect square on the left side: (x + -30)(x + -30) = 870 Calculate the square root of the right side: 29.495762408 Break this problem into two subproblems by setting (x + -30) equal to 29.495762408 and -29.495762408.Subproblem 1
x + -30 = 29.495762408 Simplifying x + -30 = 29.495762408 Reorder the terms: -30 + x = 29.495762408 Solving -30 + x = 29.495762408 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 = 29.495762408 + 30 Combine like terms: -30 + 30 = 0 0 + x = 29.495762408 + 30 x = 29.495762408 + 30 Combine like terms: 29.495762408 + 30 = 59.495762408 x = 59.495762408 Simplifying x = 59.495762408Subproblem 2
x + -30 = -29.495762408 Simplifying x + -30 = -29.495762408 Reorder the terms: -30 + x = -29.495762408 Solving -30 + x = -29.495762408 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 = -29.495762408 + 30 Combine like terms: -30 + 30 = 0 0 + x = -29.495762408 + 30 x = -29.495762408 + 30 Combine like terms: -29.495762408 + 30 = 0.504237592 x = 0.504237592 Simplifying x = 0.504237592Solution
The solution to the problem is based on the solutions from the subproblems. x = {59.495762408, 0.504237592}
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