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Simplifying x2 + 190x + -380 = 0 Reorder the terms: -380 + 190x + x2 = 0 Solving -380 + 190x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '380' to each side of the equation. -380 + 190x + 380 + x2 = 0 + 380 Reorder the terms: -380 + 380 + 190x + x2 = 0 + 380 Combine like terms: -380 + 380 = 0 0 + 190x + x2 = 0 + 380 190x + x2 = 0 + 380 Combine like terms: 0 + 380 = 380 190x + x2 = 380 The x term is 190x. Take half its coefficient (95). Square it (9025) and add it to both sides. Add '9025' to each side of the equation. 190x + 9025 + x2 = 380 + 9025 Reorder the terms: 9025 + 190x + x2 = 380 + 9025 Combine like terms: 380 + 9025 = 9405 9025 + 190x + x2 = 9405 Factor a perfect square on the left side: (x + 95)(x + 95) = 9405 Calculate the square root of the right side: 96.979379251 Break this problem into two subproblems by setting (x + 95) equal to 96.979379251 and -96.979379251.Subproblem 1
x + 95 = 96.979379251 Simplifying x + 95 = 96.979379251 Reorder the terms: 95 + x = 96.979379251 Solving 95 + x = 96.979379251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = 96.979379251 + -95 Combine like terms: 95 + -95 = 0 0 + x = 96.979379251 + -95 x = 96.979379251 + -95 Combine like terms: 96.979379251 + -95 = 1.979379251 x = 1.979379251 Simplifying x = 1.979379251Subproblem 2
x + 95 = -96.979379251 Simplifying x + 95 = -96.979379251 Reorder the terms: 95 + x = -96.979379251 Solving 95 + x = -96.979379251 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-95' to each side of the equation. 95 + -95 + x = -96.979379251 + -95 Combine like terms: 95 + -95 = 0 0 + x = -96.979379251 + -95 x = -96.979379251 + -95 Combine like terms: -96.979379251 + -95 = -191.979379251 x = -191.979379251 Simplifying x = -191.979379251Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.979379251, -191.979379251}
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