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Simplifying 0.5x2 + -1x + 8 + -332 = 0 Reorder the terms: 8 + -332 + -1x + 0.5x2 = 0 Combine like terms: 8 + -332 = -324 -324 + -1x + 0.5x2 = 0 Solving -324 + -1x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -648 + -2x + x2 = 0 Move the constant term to the right: Add '648' to each side of the equation. -648 + -2x + 648 + x2 = 0 + 648 Reorder the terms: -648 + 648 + -2x + x2 = 0 + 648 Combine like terms: -648 + 648 = 0 0 + -2x + x2 = 0 + 648 -2x + x2 = 0 + 648 Combine like terms: 0 + 648 = 648 -2x + x2 = 648 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 = 648 + 1 Reorder the terms: 1 + -2x + x2 = 648 + 1 Combine like terms: 648 + 1 = 649 1 + -2x + x2 = 649 Factor a perfect square on the left side: (x + -1)(x + -1) = 649 Calculate the square root of the right side: 25.475478406 Break this problem into two subproblems by setting (x + -1) equal to 25.475478406 and -25.475478406.Subproblem 1
x + -1 = 25.475478406 Simplifying x + -1 = 25.475478406 Reorder the terms: -1 + x = 25.475478406 Solving -1 + x = 25.475478406 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 = 25.475478406 + 1 Combine like terms: -1 + 1 = 0 0 + x = 25.475478406 + 1 x = 25.475478406 + 1 Combine like terms: 25.475478406 + 1 = 26.475478406 x = 26.475478406 Simplifying x = 26.475478406Subproblem 2
x + -1 = -25.475478406 Simplifying x + -1 = -25.475478406 Reorder the terms: -1 + x = -25.475478406 Solving -1 + x = -25.475478406 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 = -25.475478406 + 1 Combine like terms: -1 + 1 = 0 0 + x = -25.475478406 + 1 x = -25.475478406 + 1 Combine like terms: -25.475478406 + 1 = -24.475478406 x = -24.475478406 Simplifying x = -24.475478406Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.475478406, -24.475478406}
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