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Simplifying 25x2 + -30x + -116 = 0 Reorder the terms: -116 + -30x + 25x2 = 0 Solving -116 + -30x + 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'. -4.64 + -1.2x + x2 = 0 Move the constant term to the right: Add '4.64' to each side of the equation. -4.64 + -1.2x + 4.64 + x2 = 0 + 4.64 Reorder the terms: -4.64 + 4.64 + -1.2x + x2 = 0 + 4.64 Combine like terms: -4.64 + 4.64 = 0.00 0.00 + -1.2x + x2 = 0 + 4.64 -1.2x + x2 = 0 + 4.64 Combine like terms: 0 + 4.64 = 4.64 -1.2x + x2 = 4.64 The x term is -1.2x. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2x + 0.36 + x2 = 4.64 + 0.36 Reorder the terms: 0.36 + -1.2x + x2 = 4.64 + 0.36 Combine like terms: 4.64 + 0.36 = 5 0.36 + -1.2x + x2 = 5 Factor a perfect square on the left side: (x + -0.6)(x + -0.6) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (x + -0.6) equal to 2.236067978 and -2.236067978.Subproblem 1
x + -0.6 = 2.236067978 Simplifying x + -0.6 = 2.236067978 Reorder the terms: -0.6 + x = 2.236067978 Solving -0.6 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = 2.236067978 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = 2.236067978 + 0.6 x = 2.236067978 + 0.6 Combine like terms: 2.236067978 + 0.6 = 2.836067978 x = 2.836067978 Simplifying x = 2.836067978Subproblem 2
x + -0.6 = -2.236067978 Simplifying x + -0.6 = -2.236067978 Reorder the terms: -0.6 + x = -2.236067978 Solving -0.6 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + x = -2.236067978 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + x = -2.236067978 + 0.6 x = -2.236067978 + 0.6 Combine like terms: -2.236067978 + 0.6 = -1.636067978 x = -1.636067978 Simplifying x = -1.636067978Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.836067978, -1.636067978}
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