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Simplifying 2x2 + -2x = 9 Reorder the terms: -2x + 2x2 = 9 Solving -2x + 2x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -2x + 2x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -1x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -1x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -1x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -1x + x2 = 0 + 4.5 -1x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -1x + x2 = 4.5 The x term is -1x. 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. -1x + 0.25 + x2 = 4.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 4.5 + 0.25 Combine like terms: 4.5 + 0.25 = 4.75 0.25 + -1x + x2 = 4.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + -0.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + -0.5 = 2.179449472 Simplifying x + -0.5 = 2.179449472 Reorder the terms: -0.5 + x = 2.179449472 Solving -0.5 + x = 2.179449472 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 = 2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.179449472 + 0.5 x = 2.179449472 + 0.5 Combine like terms: 2.179449472 + 0.5 = 2.679449472 x = 2.679449472 Simplifying x = 2.679449472Subproblem 2
x + -0.5 = -2.179449472 Simplifying x + -0.5 = -2.179449472 Reorder the terms: -0.5 + x = -2.179449472 Solving -0.5 + x = -2.179449472 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 = -2.179449472 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.179449472 + 0.5 x = -2.179449472 + 0.5 Combine like terms: -2.179449472 + 0.5 = -1.679449472 x = -1.679449472 Simplifying x = -1.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.679449472, -1.679449472}
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