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Simplifying 6x2 + x = 3.25 Reorder the terms: x + 6x2 = 3.25 Solving x + 6x2 = 3.25 Solving for variable 'x'. Reorder the terms: -3.25 + x + 6x2 = 3.25 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 -3.25 + x + 6x2 = 0.00 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5416666667 + 0.1666666667x + x2 = 0.00 Move the constant term to the right: Add '0.5416666667' to each side of the equation. -0.5416666667 + 0.1666666667x + 0.5416666667 + x2 = 0.00 + 0.5416666667 Reorder the terms: -0.5416666667 + 0.5416666667 + 0.1666666667x + x2 = 0.00 + 0.5416666667 Combine like terms: -0.5416666667 + 0.5416666667 = 0.0000000000 0.0000000000 + 0.1666666667x + x2 = 0.00 + 0.5416666667 0.1666666667x + x2 = 0.00 + 0.5416666667 Combine like terms: 0.00 + 0.5416666667 = 0.5416666667 0.1666666667x + x2 = 0.5416666667 The x term is x. 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. 0.1666666667x + 0.25 + x2 = 0.5416666667 + 0.25 Reorder the terms: 0.25 + 0.1666666667x + x2 = 0.5416666667 + 0.25 Combine like terms: 0.5416666667 + 0.25 = 0.7916666667 0.25 + 0.1666666667x + x2 = 0.7916666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.7916666667 Calculate the square root of the right side: 0.889756521 Break this problem into two subproblems by setting (x + 0.5) equal to 0.889756521 and -0.889756521.Subproblem 1
x + 0.5 = 0.889756521 Simplifying x + 0.5 = 0.889756521 Reorder the terms: 0.5 + x = 0.889756521 Solving 0.5 + x = 0.889756521 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 = 0.889756521 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.889756521 + -0.5 x = 0.889756521 + -0.5 Combine like terms: 0.889756521 + -0.5 = 0.389756521 x = 0.389756521 Simplifying x = 0.389756521Subproblem 2
x + 0.5 = -0.889756521 Simplifying x + 0.5 = -0.889756521 Reorder the terms: 0.5 + x = -0.889756521 Solving 0.5 + x = -0.889756521 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 = -0.889756521 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.889756521 + -0.5 x = -0.889756521 + -0.5 Combine like terms: -0.889756521 + -0.5 = -1.389756521 x = -1.389756521 Simplifying x = -1.389756521Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389756521, -1.389756521}
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