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Simplifying 25x2 + -10x + -14 = 0 Reorder the terms: -14 + -10x + 25x2 = 0 Solving -14 + -10x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.56 + -0.4x + x2 = 0 Move the constant term to the right: Add '0.56' to each side of the equation. -0.56 + -0.4x + 0.56 + x2 = 0 + 0.56 Reorder the terms: -0.56 + 0.56 + -0.4x + x2 = 0 + 0.56 Combine like terms: -0.56 + 0.56 = 0.00 0.00 + -0.4x + x2 = 0 + 0.56 -0.4x + x2 = 0 + 0.56 Combine like terms: 0 + 0.56 = 0.56 -0.4x + x2 = 0.56 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = 0.56 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = 0.56 + 0.04 Combine like terms: 0.56 + 0.04 = 0.6 0.04 + -0.4x + x2 = 0.6 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.6 Calculate the square root of the right side: 0.774596669 Break this problem into two subproblems by setting (x + -0.2) equal to 0.774596669 and -0.774596669.Subproblem 1
x + -0.2 = 0.774596669 Simplifying x + -0.2 = 0.774596669 Reorder the terms: -0.2 + x = 0.774596669 Solving -0.2 + x = 0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.774596669 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.774596669 + 0.2 x = 0.774596669 + 0.2 Combine like terms: 0.774596669 + 0.2 = 0.974596669 x = 0.974596669 Simplifying x = 0.974596669Subproblem 2
x + -0.2 = -0.774596669 Simplifying x + -0.2 = -0.774596669 Reorder the terms: -0.2 + x = -0.774596669 Solving -0.2 + x = -0.774596669 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.774596669 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.774596669 + 0.2 x = -0.774596669 + 0.2 Combine like terms: -0.774596669 + 0.2 = -0.574596669 x = -0.574596669 Simplifying x = -0.574596669Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.974596669, -0.574596669}
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