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Simplifying x2 + -49x + 380 = 0 Reorder the terms: 380 + -49x + x2 = 0 Solving 380 + -49x + 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 + -49x + -380 + x2 = 0 + -380 Reorder the terms: 380 + -380 + -49x + x2 = 0 + -380 Combine like terms: 380 + -380 = 0 0 + -49x + x2 = 0 + -380 -49x + x2 = 0 + -380 Combine like terms: 0 + -380 = -380 -49x + x2 = -380 The x term is -49x. Take half its coefficient (-24.5). Square it (600.25) and add it to both sides. Add '600.25' to each side of the equation. -49x + 600.25 + x2 = -380 + 600.25 Reorder the terms: 600.25 + -49x + x2 = -380 + 600.25 Combine like terms: -380 + 600.25 = 220.25 600.25 + -49x + x2 = 220.25 Factor a perfect square on the left side: (x + -24.5)(x + -24.5) = 220.25 Calculate the square root of the right side: 14.84082208 Break this problem into two subproblems by setting (x + -24.5) equal to 14.84082208 and -14.84082208.Subproblem 1
x + -24.5 = 14.84082208 Simplifying x + -24.5 = 14.84082208 Reorder the terms: -24.5 + x = 14.84082208 Solving -24.5 + x = 14.84082208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = 14.84082208 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = 14.84082208 + 24.5 x = 14.84082208 + 24.5 Combine like terms: 14.84082208 + 24.5 = 39.34082208 x = 39.34082208 Simplifying x = 39.34082208Subproblem 2
x + -24.5 = -14.84082208 Simplifying x + -24.5 = -14.84082208 Reorder the terms: -24.5 + x = -14.84082208 Solving -24.5 + x = -14.84082208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.5' to each side of the equation. -24.5 + 24.5 + x = -14.84082208 + 24.5 Combine like terms: -24.5 + 24.5 = 0.0 0.0 + x = -14.84082208 + 24.5 x = -14.84082208 + 24.5 Combine like terms: -14.84082208 + 24.5 = 9.65917792 x = 9.65917792 Simplifying x = 9.65917792Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.34082208, 9.65917792}
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