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Simplifying 25x2 + -14x + -23 = 0 Reorder the terms: -23 + -14x + 25x2 = 0 Solving -23 + -14x + 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'. -0.92 + -0.56x + x2 = 0 Move the constant term to the right: Add '0.92' to each side of the equation. -0.92 + -0.56x + 0.92 + x2 = 0 + 0.92 Reorder the terms: -0.92 + 0.92 + -0.56x + x2 = 0 + 0.92 Combine like terms: -0.92 + 0.92 = 0.00 0.00 + -0.56x + x2 = 0 + 0.92 -0.56x + x2 = 0 + 0.92 Combine like terms: 0 + 0.92 = 0.92 -0.56x + x2 = 0.92 The x term is -0.56x. Take half its coefficient (-0.28). Square it (0.0784) and add it to both sides. Add '0.0784' to each side of the equation. -0.56x + 0.0784 + x2 = 0.92 + 0.0784 Reorder the terms: 0.0784 + -0.56x + x2 = 0.92 + 0.0784 Combine like terms: 0.92 + 0.0784 = 0.9984 0.0784 + -0.56x + x2 = 0.9984 Factor a perfect square on the left side: (x + -0.28)(x + -0.28) = 0.9984 Calculate the square root of the right side: 0.99919968 Break this problem into two subproblems by setting (x + -0.28) equal to 0.99919968 and -0.99919968.Subproblem 1
x + -0.28 = 0.99919968 Simplifying x + -0.28 = 0.99919968 Reorder the terms: -0.28 + x = 0.99919968 Solving -0.28 + x = 0.99919968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x = 0.99919968 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x = 0.99919968 + 0.28 x = 0.99919968 + 0.28 Combine like terms: 0.99919968 + 0.28 = 1.27919968 x = 1.27919968 Simplifying x = 1.27919968Subproblem 2
x + -0.28 = -0.99919968 Simplifying x + -0.28 = -0.99919968 Reorder the terms: -0.28 + x = -0.99919968 Solving -0.28 + x = -0.99919968 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.28' to each side of the equation. -0.28 + 0.28 + x = -0.99919968 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + x = -0.99919968 + 0.28 x = -0.99919968 + 0.28 Combine like terms: -0.99919968 + 0.28 = -0.71919968 x = -0.71919968 Simplifying x = -0.71919968Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.27919968, -0.71919968}
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