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Simplifying x2 + 760x = 800 Reorder the terms: 760x + x2 = 800 Solving 760x + x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 760x + x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 760x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 760x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 760x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 760x + x2 = 0 + 800 760x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 760x + x2 = 800 The x term is 760x. Take half its coefficient (380). Square it (144400) and add it to both sides. Add '144400' to each side of the equation. 760x + 144400 + x2 = 800 + 144400 Reorder the terms: 144400 + 760x + x2 = 800 + 144400 Combine like terms: 800 + 144400 = 145200 144400 + 760x + x2 = 145200 Factor a perfect square on the left side: (x + 380)(x + 380) = 145200 Calculate the square root of the right side: 381.051177665 Break this problem into two subproblems by setting (x + 380) equal to 381.051177665 and -381.051177665.Subproblem 1
x + 380 = 381.051177665 Simplifying x + 380 = 381.051177665 Reorder the terms: 380 + x = 381.051177665 Solving 380 + x = 381.051177665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-380' to each side of the equation. 380 + -380 + x = 381.051177665 + -380 Combine like terms: 380 + -380 = 0 0 + x = 381.051177665 + -380 x = 381.051177665 + -380 Combine like terms: 381.051177665 + -380 = 1.051177665 x = 1.051177665 Simplifying x = 1.051177665Subproblem 2
x + 380 = -381.051177665 Simplifying x + 380 = -381.051177665 Reorder the terms: 380 + x = -381.051177665 Solving 380 + x = -381.051177665 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-380' to each side of the equation. 380 + -380 + x = -381.051177665 + -380 Combine like terms: 380 + -380 = 0 0 + x = -381.051177665 + -380 x = -381.051177665 + -380 Combine like terms: -381.051177665 + -380 = -761.051177665 x = -761.051177665 Simplifying x = -761.051177665Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.051177665, -761.051177665}
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