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Simplifying 0 = 25x2 + 100x + 76 Reorder the terms: 0 = 76 + 100x + 25x2 Solving 0 = 76 + 100x + 25x2 Solving for variable 'x'. Combine like terms: 0 + -76 = -76 -76 + -100x + -25x2 = 76 + 100x + 25x2 + -76 + -100x + -25x2 Reorder the terms: -76 + -100x + -25x2 = 76 + -76 + 100x + -100x + 25x2 + -25x2 Combine like terms: 76 + -76 = 0 -76 + -100x + -25x2 = 0 + 100x + -100x + 25x2 + -25x2 -76 + -100x + -25x2 = 100x + -100x + 25x2 + -25x2 Combine like terms: 100x + -100x = 0 -76 + -100x + -25x2 = 0 + 25x2 + -25x2 -76 + -100x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 -76 + -100x + -25x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(76 + 100x + 25x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(76 + 100x + 25x2)' equal to zero and attempt to solve: Simplifying 76 + 100x + 25x2 = 0 Solving 76 + 100x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 3.04 + 4x + x2 = 0 Move the constant term to the right: Add '-3.04' to each side of the equation. 3.04 + 4x + -3.04 + x2 = 0 + -3.04 Reorder the terms: 3.04 + -3.04 + 4x + x2 = 0 + -3.04 Combine like terms: 3.04 + -3.04 = 0.00 0.00 + 4x + x2 = 0 + -3.04 4x + x2 = 0 + -3.04 Combine like terms: 0 + -3.04 = -3.04 4x + x2 = -3.04 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -3.04 + 4 Reorder the terms: 4 + 4x + x2 = -3.04 + 4 Combine like terms: -3.04 + 4 = 0.96 4 + 4x + x2 = 0.96 Factor a perfect square on the left side: (x + 2)(x + 2) = 0.96 Calculate the square root of the right side: 0.979795897 Break this problem into two subproblems by setting (x + 2) equal to 0.979795897 and -0.979795897.Subproblem 1
x + 2 = 0.979795897 Simplifying x + 2 = 0.979795897 Reorder the terms: 2 + x = 0.979795897 Solving 2 + x = 0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0.979795897 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0.979795897 + -2 x = 0.979795897 + -2 Combine like terms: 0.979795897 + -2 = -1.020204103 x = -1.020204103 Simplifying x = -1.020204103Subproblem 2
x + 2 = -0.979795897 Simplifying x + 2 = -0.979795897 Reorder the terms: 2 + x = -0.979795897 Solving 2 + x = -0.979795897 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -0.979795897 + -2 Combine like terms: 2 + -2 = 0 0 + x = -0.979795897 + -2 x = -0.979795897 + -2 Combine like terms: -0.979795897 + -2 = -2.979795897 x = -2.979795897 Simplifying x = -2.979795897Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.020204103, -2.979795897}Solution
x = {-1.020204103, -2.979795897}
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