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Simplifying x2 + 20x = -3 Reorder the terms: 20x + x2 = -3 Solving 20x + x2 = -3 Solving for variable 'x'. Reorder the terms: 3 + 20x + x2 = -3 + 3 Combine like terms: -3 + 3 = 0 3 + 20x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 20x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 20x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 20x + x2 = 0 + -3 20x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 20x + x2 = -3 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 = -3 + 100 Reorder the terms: 100 + 20x + x2 = -3 + 100 Combine like terms: -3 + 100 = 97 100 + 20x + x2 = 97 Factor a perfect square on the left side: (x + 10)(x + 10) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 10) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 10 = 9.848857802 Simplifying x + 10 = 9.848857802 Reorder the terms: 10 + x = 9.848857802 Solving 10 + x = 9.848857802 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 = 9.848857802 + -10 Combine like terms: 10 + -10 = 0 0 + x = 9.848857802 + -10 x = 9.848857802 + -10 Combine like terms: 9.848857802 + -10 = -0.151142198 x = -0.151142198 Simplifying x = -0.151142198Subproblem 2
x + 10 = -9.848857802 Simplifying x + 10 = -9.848857802 Reorder the terms: 10 + x = -9.848857802 Solving 10 + x = -9.848857802 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 = -9.848857802 + -10 Combine like terms: 10 + -10 = 0 0 + x = -9.848857802 + -10 x = -9.848857802 + -10 Combine like terms: -9.848857802 + -10 = -19.848857802 x = -19.848857802 Simplifying x = -19.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.151142198, -19.848857802}
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