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Simplifying -200x2 + 100x + 31 = 0 Reorder the terms: 31 + 100x + -200x2 = 0 Solving 31 + 100x + -200x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -200 the coefficient of the squared term: Divide each side by '-200'. -0.155 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.155' to each side of the equation. -0.155 + -0.5x + 0.155 + x2 = 0 + 0.155 Reorder the terms: -0.155 + 0.155 + -0.5x + x2 = 0 + 0.155 Combine like terms: -0.155 + 0.155 = 0.000 0.000 + -0.5x + x2 = 0 + 0.155 -0.5x + x2 = 0 + 0.155 Combine like terms: 0 + 0.155 = 0.155 -0.5x + x2 = 0.155 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.155 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.155 + 0.0625 Combine like terms: 0.155 + 0.0625 = 0.2175 0.0625 + -0.5x + x2 = 0.2175 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.2175 Calculate the square root of the right side: 0.466368953 Break this problem into two subproblems by setting (x + -0.25) equal to 0.466368953 and -0.466368953.Subproblem 1
x + -0.25 = 0.466368953 Simplifying x + -0.25 = 0.466368953 Reorder the terms: -0.25 + x = 0.466368953 Solving -0.25 + x = 0.466368953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.466368953 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.466368953 + 0.25 x = 0.466368953 + 0.25 Combine like terms: 0.466368953 + 0.25 = 0.716368953 x = 0.716368953 Simplifying x = 0.716368953Subproblem 2
x + -0.25 = -0.466368953 Simplifying x + -0.25 = -0.466368953 Reorder the terms: -0.25 + x = -0.466368953 Solving -0.25 + x = -0.466368953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.466368953 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.466368953 + 0.25 x = -0.466368953 + 0.25 Combine like terms: -0.466368953 + 0.25 = -0.216368953 x = -0.216368953 Simplifying x = -0.216368953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.716368953, -0.216368953}
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