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Simplifying 2x2 + -10x = 45 Reorder the terms: -10x + 2x2 = 45 Solving -10x + 2x2 = 45 Solving for variable 'x'. Reorder the terms: -45 + -10x + 2x2 = 45 + -45 Combine like terms: 45 + -45 = 0 -45 + -10x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -22.5 + -5x + x2 = 0 Move the constant term to the right: Add '22.5' to each side of the equation. -22.5 + -5x + 22.5 + x2 = 0 + 22.5 Reorder the terms: -22.5 + 22.5 + -5x + x2 = 0 + 22.5 Combine like terms: -22.5 + 22.5 = 0.0 0.0 + -5x + x2 = 0 + 22.5 -5x + x2 = 0 + 22.5 Combine like terms: 0 + 22.5 = 22.5 -5x + x2 = 22.5 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 = 22.5 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 22.5 + 6.25 Combine like terms: 22.5 + 6.25 = 28.75 6.25 + -5x + x2 = 28.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 28.75 Calculate the square root of the right side: 5.361902647 Break this problem into two subproblems by setting (x + -2.5) equal to 5.361902647 and -5.361902647.Subproblem 1
x + -2.5 = 5.361902647 Simplifying x + -2.5 = 5.361902647 Reorder the terms: -2.5 + x = 5.361902647 Solving -2.5 + x = 5.361902647 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 = 5.361902647 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.361902647 + 2.5 x = 5.361902647 + 2.5 Combine like terms: 5.361902647 + 2.5 = 7.861902647 x = 7.861902647 Simplifying x = 7.861902647Subproblem 2
x + -2.5 = -5.361902647 Simplifying x + -2.5 = -5.361902647 Reorder the terms: -2.5 + x = -5.361902647 Solving -2.5 + x = -5.361902647 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 = -5.361902647 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.361902647 + 2.5 x = -5.361902647 + 2.5 Combine like terms: -5.361902647 + 2.5 = -2.861902647 x = -2.861902647 Simplifying x = -2.861902647Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.861902647, -2.861902647}
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