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Simplifying 25x2 + -200x + 10 = 0 Reorder the terms: 10 + -200x + 25x2 = 0 Solving 10 + -200x + 25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + -40x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + -40x + 5x2)' equal to zero and attempt to solve: Simplifying 2 + -40x + 5x2 = 0 Solving 2 + -40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -8x + x2 = 0 + -0.4 -8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -8x + x2 = -0.4 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -0.4 + 16 Reorder the terms: 16 + -8x + x2 = -0.4 + 16 Combine like terms: -0.4 + 16 = 15.6 16 + -8x + x2 = 15.6 Factor a perfect square on the left side: (x + -4)(x + -4) = 15.6 Calculate the square root of the right side: 3.949683532 Break this problem into two subproblems by setting (x + -4) equal to 3.949683532 and -3.949683532.Subproblem 1
x + -4 = 3.949683532 Simplifying x + -4 = 3.949683532 Reorder the terms: -4 + x = 3.949683532 Solving -4 + x = 3.949683532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.949683532 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.949683532 + 4 x = 3.949683532 + 4 Combine like terms: 3.949683532 + 4 = 7.949683532 x = 7.949683532 Simplifying x = 7.949683532Subproblem 2
x + -4 = -3.949683532 Simplifying x + -4 = -3.949683532 Reorder the terms: -4 + x = -3.949683532 Solving -4 + x = -3.949683532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.949683532 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.949683532 + 4 x = -3.949683532 + 4 Combine like terms: -3.949683532 + 4 = 0.050316468 x = 0.050316468 Simplifying x = 0.050316468Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.949683532, 0.050316468}Solution
x = {7.949683532, 0.050316468}
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