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Simplifying 2x2 + -9 = 10x Reorder the terms: -9 + 2x2 = 10x Solving -9 + 2x2 = 10x Solving for variable 'x'. Reorder the terms: -9 + -10x + 2x2 = 10x + -10x Combine like terms: 10x + -10x = 0 -9 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + -5x + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + -5x + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + -5x + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + -5x + x2 = 0 + 4.5 -5x + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 -5x + x2 = 4.5 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 4.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 4.5 + 6.25 Combine like terms: 4.5 + 6.25 = 10.75 6.25 + -5x + x2 = 10.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + -2.5) equal to 3.278719262 and -3.278719262.Subproblem 1
x + -2.5 = 3.278719262 Simplifying x + -2.5 = 3.278719262 Reorder the terms: -2.5 + x = 3.278719262 Solving -2.5 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.278719262 + 2.5 x = 3.278719262 + 2.5 Combine like terms: 3.278719262 + 2.5 = 5.778719262 x = 5.778719262 Simplifying x = 5.778719262Subproblem 2
x + -2.5 = -3.278719262 Simplifying x + -2.5 = -3.278719262 Reorder the terms: -2.5 + x = -3.278719262 Solving -2.5 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -3.278719262 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.278719262 + 2.5 x = -3.278719262 + 2.5 Combine like terms: -3.278719262 + 2.5 = -0.778719262 x = -0.778719262 Simplifying x = -0.778719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.778719262, -0.778719262}
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