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Simplifying 14 = 2x2 + x Reorder the terms: 14 = x + 2x2 Solving 14 = x + 2x2 Solving for variable 'x'. Reorder the terms: 14 + -1x + -2x2 = x + -1x + 2x2 + -2x2 Combine like terms: x + -1x = 0 14 + -1x + -2x2 = 0 + 2x2 + -2x2 14 + -1x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 14 + -1x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -7 + 0.5x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + 0.5x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + 0.5x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 0.5x + x2 = 0 + 7 0.5x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 0.5x + x2 = 7 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 = 7 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 7 + 0.0625 Combine like terms: 7 + 0.0625 = 7.0625 0.0625 + 0.5x + x2 = 7.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 7.0625 Calculate the square root of the right side: 2.657536453 Break this problem into two subproblems by setting (x + 0.25) equal to 2.657536453 and -2.657536453.Subproblem 1
x + 0.25 = 2.657536453 Simplifying x + 0.25 = 2.657536453 Reorder the terms: 0.25 + x = 2.657536453 Solving 0.25 + x = 2.657536453 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 = 2.657536453 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 2.657536453 + -0.25 x = 2.657536453 + -0.25 Combine like terms: 2.657536453 + -0.25 = 2.407536453 x = 2.407536453 Simplifying x = 2.407536453Subproblem 2
x + 0.25 = -2.657536453 Simplifying x + 0.25 = -2.657536453 Reorder the terms: 0.25 + x = -2.657536453 Solving 0.25 + x = -2.657536453 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 = -2.657536453 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -2.657536453 + -0.25 x = -2.657536453 + -0.25 Combine like terms: -2.657536453 + -0.25 = -2.907536453 x = -2.907536453 Simplifying x = -2.907536453Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.407536453, -2.907536453}
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