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Simplifying x2 + 2x + -672 = 0 Reorder the terms: -672 + 2x + x2 = 0 Solving -672 + 2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '672' to each side of the equation. -672 + 2x + 672 + x2 = 0 + 672 Reorder the terms: -672 + 672 + 2x + x2 = 0 + 672 Combine like terms: -672 + 672 = 0 0 + 2x + x2 = 0 + 672 2x + x2 = 0 + 672 Combine like terms: 0 + 672 = 672 2x + x2 = 672 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 672 + 1 Reorder the terms: 1 + 2x + x2 = 672 + 1 Combine like terms: 672 + 1 = 673 1 + 2x + x2 = 673 Factor a perfect square on the left side: (x + 1)(x + 1) = 673 Calculate the square root of the right side: 25.942243542 Break this problem into two subproblems by setting (x + 1) equal to 25.942243542 and -25.942243542.Subproblem 1
x + 1 = 25.942243542 Simplifying x + 1 = 25.942243542 Reorder the terms: 1 + x = 25.942243542 Solving 1 + x = 25.942243542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 25.942243542 + -1 Combine like terms: 1 + -1 = 0 0 + x = 25.942243542 + -1 x = 25.942243542 + -1 Combine like terms: 25.942243542 + -1 = 24.942243542 x = 24.942243542 Simplifying x = 24.942243542Subproblem 2
x + 1 = -25.942243542 Simplifying x + 1 = -25.942243542 Reorder the terms: 1 + x = -25.942243542 Solving 1 + x = -25.942243542 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -25.942243542 + -1 Combine like terms: 1 + -1 = 0 0 + x = -25.942243542 + -1 x = -25.942243542 + -1 Combine like terms: -25.942243542 + -1 = -26.942243542 x = -26.942243542 Simplifying x = -26.942243542Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.942243542, -26.942243542}
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