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Simplifying 2x + 35.75 = x2 Reorder the terms: 35.75 + 2x = x2 Solving 35.75 + 2x = x2 Solving for variable 'x'. Combine like terms: x2 + -1x2 = 0 35.75 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -35.75 + -2x + x2 = 0 Move the constant term to the right: Add '35.75' to each side of the equation. -35.75 + -2x + 35.75 + x2 = 0 + 35.75 Reorder the terms: -35.75 + 35.75 + -2x + x2 = 0 + 35.75 Combine like terms: -35.75 + 35.75 = 0.00 0.00 + -2x + x2 = 0 + 35.75 -2x + x2 = 0 + 35.75 Combine like terms: 0 + 35.75 = 35.75 -2x + x2 = 35.75 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 = 35.75 + 1 Reorder the terms: 1 + -2x + x2 = 35.75 + 1 Combine like terms: 35.75 + 1 = 36.75 1 + -2x + x2 = 36.75 Factor a perfect square on the left side: (x + -1)(x + -1) = 36.75 Calculate the square root of the right side: 6.062177826 Break this problem into two subproblems by setting (x + -1) equal to 6.062177826 and -6.062177826.Subproblem 1
x + -1 = 6.062177826 Simplifying x + -1 = 6.062177826 Reorder the terms: -1 + x = 6.062177826 Solving -1 + x = 6.062177826 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 = 6.062177826 + 1 Combine like terms: -1 + 1 = 0 0 + x = 6.062177826 + 1 x = 6.062177826 + 1 Combine like terms: 6.062177826 + 1 = 7.062177826 x = 7.062177826 Simplifying x = 7.062177826Subproblem 2
x + -1 = -6.062177826 Simplifying x + -1 = -6.062177826 Reorder the terms: -1 + x = -6.062177826 Solving -1 + x = -6.062177826 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 = -6.062177826 + 1 Combine like terms: -1 + 1 = 0 0 + x = -6.062177826 + 1 x = -6.062177826 + 1 Combine like terms: -6.062177826 + 1 = -5.062177826 x = -5.062177826 Simplifying x = -5.062177826Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.062177826, -5.062177826}
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