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Simplifying x2 + -20x + -840 = 0 Reorder the terms: -840 + -20x + x2 = 0 Solving -840 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '840' to each side of the equation. -840 + -20x + 840 + x2 = 0 + 840 Reorder the terms: -840 + 840 + -20x + x2 = 0 + 840 Combine like terms: -840 + 840 = 0 0 + -20x + x2 = 0 + 840 -20x + x2 = 0 + 840 Combine like terms: 0 + 840 = 840 -20x + x2 = 840 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = 840 + 100 Reorder the terms: 100 + -20x + x2 = 840 + 100 Combine like terms: 840 + 100 = 940 100 + -20x + x2 = 940 Factor a perfect square on the left side: (x + -10)(x + -10) = 940 Calculate the square root of the right side: 30.659419434 Break this problem into two subproblems by setting (x + -10) equal to 30.659419434 and -30.659419434.Subproblem 1
x + -10 = 30.659419434 Simplifying x + -10 = 30.659419434 Reorder the terms: -10 + x = 30.659419434 Solving -10 + x = 30.659419434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 30.659419434 + 10 Combine like terms: -10 + 10 = 0 0 + x = 30.659419434 + 10 x = 30.659419434 + 10 Combine like terms: 30.659419434 + 10 = 40.659419434 x = 40.659419434 Simplifying x = 40.659419434Subproblem 2
x + -10 = -30.659419434 Simplifying x + -10 = -30.659419434 Reorder the terms: -10 + x = -30.659419434 Solving -10 + x = -30.659419434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -30.659419434 + 10 Combine like terms: -10 + 10 = 0 0 + x = -30.659419434 + 10 x = -30.659419434 + 10 Combine like terms: -30.659419434 + 10 = -20.659419434 x = -20.659419434 Simplifying x = -20.659419434Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.659419434, -20.659419434}
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