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Simplifying x2 + 60x + -40 = 0 Reorder the terms: -40 + 60x + x2 = 0 Solving -40 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 60x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 60x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 60x + x2 = 0 + 40 60x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 60x + x2 = 40 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 = 40 + 900 Reorder the terms: 900 + 60x + x2 = 40 + 900 Combine like terms: 40 + 900 = 940 900 + 60x + x2 = 940 Factor a perfect square on the left side: (x + 30)(x + 30) = 940 Calculate the square root of the right side: 30.659419434 Break this problem into two subproblems by setting (x + 30) equal to 30.659419434 and -30.659419434.Subproblem 1
x + 30 = 30.659419434 Simplifying x + 30 = 30.659419434 Reorder the terms: 30 + x = 30.659419434 Solving 30 + x = 30.659419434 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 = 30.659419434 + -30 Combine like terms: 30 + -30 = 0 0 + x = 30.659419434 + -30 x = 30.659419434 + -30 Combine like terms: 30.659419434 + -30 = 0.659419434 x = 0.659419434 Simplifying x = 0.659419434Subproblem 2
x + 30 = -30.659419434 Simplifying x + 30 = -30.659419434 Reorder the terms: 30 + x = -30.659419434 Solving 30 + x = -30.659419434 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 = -30.659419434 + -30 Combine like terms: 30 + -30 = 0 0 + x = -30.659419434 + -30 x = -30.659419434 + -30 Combine like terms: -30.659419434 + -30 = -60.659419434 x = -60.659419434 Simplifying x = -60.659419434Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.659419434, -60.659419434}
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