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Simplifying -1x2 + 2x + 12.5 = 0 Reorder the terms: 12.5 + 2x + -1x2 = 0 Solving 12.5 + 2x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -12.5 + -2x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -2x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -2x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -2x + x2 = 0 + 12.5 -2x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -2x + x2 = 12.5 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 = 12.5 + 1 Reorder the terms: 1 + -2x + x2 = 12.5 + 1 Combine like terms: 12.5 + 1 = 13.5 1 + -2x + x2 = 13.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 13.5 Calculate the square root of the right side: 3.674234614 Break this problem into two subproblems by setting (x + -1) equal to 3.674234614 and -3.674234614.Subproblem 1
x + -1 = 3.674234614 Simplifying x + -1 = 3.674234614 Reorder the terms: -1 + x = 3.674234614 Solving -1 + x = 3.674234614 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 = 3.674234614 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.674234614 + 1 x = 3.674234614 + 1 Combine like terms: 3.674234614 + 1 = 4.674234614 x = 4.674234614 Simplifying x = 4.674234614Subproblem 2
x + -1 = -3.674234614 Simplifying x + -1 = -3.674234614 Reorder the terms: -1 + x = -3.674234614 Solving -1 + x = -3.674234614 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 = -3.674234614 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.674234614 + 1 x = -3.674234614 + 1 Combine like terms: -3.674234614 + 1 = -2.674234614 x = -2.674234614 Simplifying x = -2.674234614Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.674234614, -2.674234614}
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