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Simplifying x + 2x2 + -10 + 15 = 320 Reorder the terms: -10 + 15 + x + 2x2 = 320 Combine like terms: -10 + 15 = 5 5 + x + 2x2 = 320 Solving 5 + x + 2x2 = 320 Solving for variable 'x'. Reorder the terms: 5 + -320 + x + 2x2 = 320 + -320 Combine like terms: 5 + -320 = -315 -315 + x + 2x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -315 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -157.5 + 0.5x + x2 = 0 Move the constant term to the right: Add '157.5' to each side of the equation. -157.5 + 0.5x + 157.5 + x2 = 0 + 157.5 Reorder the terms: -157.5 + 157.5 + 0.5x + x2 = 0 + 157.5 Combine like terms: -157.5 + 157.5 = 0.0 0.0 + 0.5x + x2 = 0 + 157.5 0.5x + x2 = 0 + 157.5 Combine like terms: 0 + 157.5 = 157.5 0.5x + x2 = 157.5 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. 0.5x + 0.25 + x2 = 157.5 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 157.5 + 0.25 Combine like terms: 157.5 + 0.25 = 157.75 0.25 + 0.5x + x2 = 157.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 157.75 Calculate the square root of the right side: 12.559856687 Break this problem into two subproblems by setting (x + 0.5) equal to 12.559856687 and -12.559856687.Subproblem 1
x + 0.5 = 12.559856687 Simplifying x + 0.5 = 12.559856687 Reorder the terms: 0.5 + x = 12.559856687 Solving 0.5 + x = 12.559856687 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 = 12.559856687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 12.559856687 + -0.5 x = 12.559856687 + -0.5 Combine like terms: 12.559856687 + -0.5 = 12.059856687 x = 12.059856687 Simplifying x = 12.059856687Subproblem 2
x + 0.5 = -12.559856687 Simplifying x + 0.5 = -12.559856687 Reorder the terms: 0.5 + x = -12.559856687 Solving 0.5 + x = -12.559856687 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 = -12.559856687 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -12.559856687 + -0.5 x = -12.559856687 + -0.5 Combine like terms: -12.559856687 + -0.5 = -13.059856687 x = -13.059856687 Simplifying x = -13.059856687Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.059856687, -13.059856687}
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