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Simplifying 2x2 + 6x = 315 Reorder the terms: 6x + 2x2 = 315 Solving 6x + 2x2 = 315 Solving for variable 'x'. Reorder the terms: -315 + 6x + 2x2 = 315 + -315 Combine like terms: 315 + -315 = 0 -315 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -157.5 + 3x + x2 = 0 Move the constant term to the right: Add '157.5' to each side of the equation. -157.5 + 3x + 157.5 + x2 = 0 + 157.5 Reorder the terms: -157.5 + 157.5 + 3x + x2 = 0 + 157.5 Combine like terms: -157.5 + 157.5 = 0.0 0.0 + 3x + x2 = 0 + 157.5 3x + x2 = 0 + 157.5 Combine like terms: 0 + 157.5 = 157.5 3x + x2 = 157.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 157.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 157.5 + 2.25 Combine like terms: 157.5 + 2.25 = 159.75 2.25 + 3x + x2 = 159.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 159.75 Calculate the square root of the right side: 12.63922466 Break this problem into two subproblems by setting (x + 1.5) equal to 12.63922466 and -12.63922466.Subproblem 1
x + 1.5 = 12.63922466 Simplifying x + 1.5 = 12.63922466 Reorder the terms: 1.5 + x = 12.63922466 Solving 1.5 + x = 12.63922466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 12.63922466 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 12.63922466 + -1.5 x = 12.63922466 + -1.5 Combine like terms: 12.63922466 + -1.5 = 11.13922466 x = 11.13922466 Simplifying x = 11.13922466Subproblem 2
x + 1.5 = -12.63922466 Simplifying x + 1.5 = -12.63922466 Reorder the terms: 1.5 + x = -12.63922466 Solving 1.5 + x = -12.63922466 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -12.63922466 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -12.63922466 + -1.5 x = -12.63922466 + -1.5 Combine like terms: -12.63922466 + -1.5 = -14.13922466 x = -14.13922466 Simplifying x = -14.13922466Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.13922466, -14.13922466}
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