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Simplifying 0.5x2 + -0.5x + 18 = 25 Reorder the terms: 18 + -0.5x + 0.5x2 = 25 Solving 18 + -0.5x + 0.5x2 = 25 Solving for variable 'x'. Reorder the terms: 18 + -25 + -0.5x + 0.5x2 = 25 + -25 Combine like terms: 18 + -25 = -7 -7 + -0.5x + 0.5x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -7 + -0.5x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -14 + -1x + x2 = 0 Move the constant term to the right: Add '14' to each side of the equation. -14 + -1x + 14 + x2 = 0 + 14 Reorder the terms: -14 + 14 + -1x + x2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + -1x + x2 = 0 + 14 -1x + x2 = 0 + 14 Combine like terms: 0 + 14 = 14 -1x + x2 = 14 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 14 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 14 + 0.25 Combine like terms: 14 + 0.25 = 14.25 0.25 + -1x + x2 = 14.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 14.25 Calculate the square root of the right side: 3.774917218 Break this problem into two subproblems by setting (x + -0.5) equal to 3.774917218 and -3.774917218.Subproblem 1
x + -0.5 = 3.774917218 Simplifying x + -0.5 = 3.774917218 Reorder the terms: -0.5 + x = 3.774917218 Solving -0.5 + x = 3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.774917218 + 0.5 x = 3.774917218 + 0.5 Combine like terms: 3.774917218 + 0.5 = 4.274917218 x = 4.274917218 Simplifying x = 4.274917218Subproblem 2
x + -0.5 = -3.774917218 Simplifying x + -0.5 = -3.774917218 Reorder the terms: -0.5 + x = -3.774917218 Solving -0.5 + x = -3.774917218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.774917218 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.774917218 + 0.5 x = -3.774917218 + 0.5 Combine like terms: -3.774917218 + 0.5 = -3.274917218 x = -3.274917218 Simplifying x = -3.274917218Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.274917218, -3.274917218}
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