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Simplifying 2x2 + -20x + 7 = 0 Reorder the terms: 7 + -20x + 2x2 = 0 Solving 7 + -20x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3.5 + -10x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -10x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -10x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -10x + x2 = 0 + -3.5 -10x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -10x + x2 = -3.5 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -3.5 + 25 Reorder the terms: 25 + -10x + x2 = -3.5 + 25 Combine like terms: -3.5 + 25 = 21.5 25 + -10x + x2 = 21.5 Factor a perfect square on the left side: (x + -5)(x + -5) = 21.5 Calculate the square root of the right side: 4.636809248 Break this problem into two subproblems by setting (x + -5) equal to 4.636809248 and -4.636809248.Subproblem 1
x + -5 = 4.636809248 Simplifying x + -5 = 4.636809248 Reorder the terms: -5 + x = 4.636809248 Solving -5 + x = 4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 4.636809248 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4.636809248 + 5 x = 4.636809248 + 5 Combine like terms: 4.636809248 + 5 = 9.636809248 x = 9.636809248 Simplifying x = 9.636809248Subproblem 2
x + -5 = -4.636809248 Simplifying x + -5 = -4.636809248 Reorder the terms: -5 + x = -4.636809248 Solving -5 + x = -4.636809248 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -4.636809248 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4.636809248 + 5 x = -4.636809248 + 5 Combine like terms: -4.636809248 + 5 = 0.363190752 x = 0.363190752 Simplifying x = 0.363190752Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.636809248, 0.363190752}
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