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Simplifying x2 + 89 = -20x Reorder the terms: 89 + x2 = -20x Solving 89 + x2 = -20x Solving for variable 'x'. Reorder the terms: 89 + 20x + x2 = -20x + 20x Combine like terms: -20x + 20x = 0 89 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-89' to each side of the equation. 89 + 20x + -89 + x2 = 0 + -89 Reorder the terms: 89 + -89 + 20x + x2 = 0 + -89 Combine like terms: 89 + -89 = 0 0 + 20x + x2 = 0 + -89 20x + x2 = 0 + -89 Combine like terms: 0 + -89 = -89 20x + x2 = -89 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 = -89 + 100 Reorder the terms: 100 + 20x + x2 = -89 + 100 Combine like terms: -89 + 100 = 11 100 + 20x + x2 = 11 Factor a perfect square on the left side: (x + 10)(x + 10) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 10) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 10 = 3.31662479 Simplifying x + 10 = 3.31662479 Reorder the terms: 10 + x = 3.31662479 Solving 10 + x = 3.31662479 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 = 3.31662479 + -10 Combine like terms: 10 + -10 = 0 0 + x = 3.31662479 + -10 x = 3.31662479 + -10 Combine like terms: 3.31662479 + -10 = -6.68337521 x = -6.68337521 Simplifying x = -6.68337521Subproblem 2
x + 10 = -3.31662479 Simplifying x + 10 = -3.31662479 Reorder the terms: 10 + x = -3.31662479 Solving 10 + x = -3.31662479 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 = -3.31662479 + -10 Combine like terms: 10 + -10 = 0 0 + x = -3.31662479 + -10 x = -3.31662479 + -10 Combine like terms: -3.31662479 + -10 = -13.31662479 x = -13.31662479 Simplifying x = -13.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {-6.68337521, -13.31662479}
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