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Simplifying 2x2 + -6x + 9 = 340 Reorder the terms: 9 + -6x + 2x2 = 340 Solving 9 + -6x + 2x2 = 340 Solving for variable 'x'. Reorder the terms: 9 + -340 + -6x + 2x2 = 340 + -340 Combine like terms: 9 + -340 = -331 -331 + -6x + 2x2 = 340 + -340 Combine like terms: 340 + -340 = 0 -331 + -6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -165.5 + -3x + x2 = 0 Move the constant term to the right: Add '165.5' to each side of the equation. -165.5 + -3x + 165.5 + x2 = 0 + 165.5 Reorder the terms: -165.5 + 165.5 + -3x + x2 = 0 + 165.5 Combine like terms: -165.5 + 165.5 = 0.0 0.0 + -3x + x2 = 0 + 165.5 -3x + x2 = 0 + 165.5 Combine like terms: 0 + 165.5 = 165.5 -3x + x2 = 165.5 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 = 165.5 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 165.5 + 2.25 Combine like terms: 165.5 + 2.25 = 167.75 2.25 + -3x + x2 = 167.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 167.75 Calculate the square root of the right side: 12.951833847 Break this problem into two subproblems by setting (x + -1.5) equal to 12.951833847 and -12.951833847.Subproblem 1
x + -1.5 = 12.951833847 Simplifying x + -1.5 = 12.951833847 Reorder the terms: -1.5 + x = 12.951833847 Solving -1.5 + x = 12.951833847 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 = 12.951833847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 12.951833847 + 1.5 x = 12.951833847 + 1.5 Combine like terms: 12.951833847 + 1.5 = 14.451833847 x = 14.451833847 Simplifying x = 14.451833847Subproblem 2
x + -1.5 = -12.951833847 Simplifying x + -1.5 = -12.951833847 Reorder the terms: -1.5 + x = -12.951833847 Solving -1.5 + x = -12.951833847 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 = -12.951833847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -12.951833847 + 1.5 x = -12.951833847 + 1.5 Combine like terms: -12.951833847 + 1.5 = -11.451833847 x = -11.451833847 Simplifying x = -11.451833847Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.451833847, -11.451833847}
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