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Simplifying x2 + 20x + -53 = 0 Reorder the terms: -53 + 20x + x2 = 0 Solving -53 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 20x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 20x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 20x + x2 = 0 + 53 20x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 20x + x2 = 53 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 = 53 + 100 Reorder the terms: 100 + 20x + x2 = 53 + 100 Combine like terms: 53 + 100 = 153 100 + 20x + x2 = 153 Factor a perfect square on the left side: (x + 10)(x + 10) = 153 Calculate the square root of the right side: 12.369316877 Break this problem into two subproblems by setting (x + 10) equal to 12.369316877 and -12.369316877.Subproblem 1
x + 10 = 12.369316877 Simplifying x + 10 = 12.369316877 Reorder the terms: 10 + x = 12.369316877 Solving 10 + x = 12.369316877 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 = 12.369316877 + -10 Combine like terms: 10 + -10 = 0 0 + x = 12.369316877 + -10 x = 12.369316877 + -10 Combine like terms: 12.369316877 + -10 = 2.369316877 x = 2.369316877 Simplifying x = 2.369316877Subproblem 2
x + 10 = -12.369316877 Simplifying x + 10 = -12.369316877 Reorder the terms: 10 + x = -12.369316877 Solving 10 + x = -12.369316877 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 = -12.369316877 + -10 Combine like terms: 10 + -10 = 0 0 + x = -12.369316877 + -10 x = -12.369316877 + -10 Combine like terms: -12.369316877 + -10 = -22.369316877 x = -22.369316877 Simplifying x = -22.369316877Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.369316877, -22.369316877}
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