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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 = 930 900 + -60x + x2 = 930 Factor a perfect square on the left side: (x + -30)(x + -30) = 930 Calculate the square root of the right side: 30.495901364 Break this problem into two subproblems by setting (x + -30) equal to 30.495901364 and -30.495901364.Subproblem 1
x + -30 = 30.495901364 Simplifying x + -30 = 30.495901364 Reorder the terms: -30 + x = 30.495901364 Solving -30 + x = 30.495901364 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 = 30.495901364 + 30 Combine like terms: -30 + 30 = 0 0 + x = 30.495901364 + 30 x = 30.495901364 + 30 Combine like terms: 30.495901364 + 30 = 60.495901364 x = 60.495901364 Simplifying x = 60.495901364Subproblem 2
x + -30 = -30.495901364 Simplifying x + -30 = -30.495901364 Reorder the terms: -30 + x = -30.495901364 Solving -30 + x = -30.495901364 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 = -30.495901364 + 30 Combine like terms: -30 + 30 = 0 0 + x = -30.495901364 + 30 x = -30.495901364 + 30 Combine like terms: -30.495901364 + 30 = -0.495901364 x = -0.495901364 Simplifying x = -0.495901364Solution
The solution to the problem is based on the solutions from the subproblems. x = {60.495901364, -0.495901364}
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