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Simplifying 2x2 + -40x + 25 = 0 Reorder the terms: 25 + -40x + 2x2 = 0 Solving 25 + -40x + 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'. 12.5 + -20x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -20x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -20x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -20x + x2 = 0 + -12.5 -20x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -20x + x2 = -12.5 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -12.5 + 100 Reorder the terms: 100 + -20x + x2 = -12.5 + 100 Combine like terms: -12.5 + 100 = 87.5 100 + -20x + x2 = 87.5 Factor a perfect square on the left side: (x + -10)(x + -10) = 87.5 Calculate the square root of the right side: 9.354143467 Break this problem into two subproblems by setting (x + -10) equal to 9.354143467 and -9.354143467.Subproblem 1
x + -10 = 9.354143467 Simplifying x + -10 = 9.354143467 Reorder the terms: -10 + x = 9.354143467 Solving -10 + x = 9.354143467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.354143467 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.354143467 + 10 x = 9.354143467 + 10 Combine like terms: 9.354143467 + 10 = 19.354143467 x = 19.354143467 Simplifying x = 19.354143467Subproblem 2
x + -10 = -9.354143467 Simplifying x + -10 = -9.354143467 Reorder the terms: -10 + x = -9.354143467 Solving -10 + x = -9.354143467 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.354143467 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.354143467 + 10 x = -9.354143467 + 10 Combine like terms: -9.354143467 + 10 = 0.645856533 x = 0.645856533 Simplifying x = 0.645856533Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.354143467, 0.645856533}
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