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Simplifying 2x * 3x + -5 = 25x Reorder the terms for easier multiplication: 2 * 3x * x + -5 = 25x Multiply 2 * 3 6x * x + -5 = 25x Multiply x * x 6x2 + -5 = 25x Reorder the terms: -5 + 6x2 = 25x Solving -5 + 6x2 = 25x Solving for variable 'x'. Reorder the terms: -5 + -25x + 6x2 = 25x + -25x Combine like terms: 25x + -25x = 0 -5 + -25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.8333333333 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '0.8333333333' to each side of the equation. -0.8333333333 + -4.166666667x + 0.8333333333 + x2 = 0 + 0.8333333333 Reorder the terms: -0.8333333333 + 0.8333333333 + -4.166666667x + x2 = 0 + 0.8333333333 Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000 0.0000000000 + -4.166666667x + x2 = 0 + 0.8333333333 -4.166666667x + x2 = 0 + 0.8333333333 Combine like terms: 0 + 0.8333333333 = 0.8333333333 -4.166666667x + x2 = 0.8333333333 The x term is -4.166666667x. Take half its coefficient (-2.083333334). Square it (4.340277781) and add it to both sides. Add '4.340277781' to each side of the equation. -4.166666667x + 4.340277781 + x2 = 0.8333333333 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = 0.8333333333 + 4.340277781 Combine like terms: 0.8333333333 + 4.340277781 = 5.1736111143 4.340277781 + -4.166666667x + x2 = 5.1736111143 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 5.1736111143 Calculate the square root of the right side: 2.274557345 Break this problem into two subproblems by setting (x + -2.083333334) equal to 2.274557345 and -2.274557345.Subproblem 1
x + -2.083333334 = 2.274557345 Simplifying x + -2.083333334 = 2.274557345 Reorder the terms: -2.083333334 + x = 2.274557345 Solving -2.083333334 + x = 2.274557345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = 2.274557345 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 2.274557345 + 2.083333334 x = 2.274557345 + 2.083333334 Combine like terms: 2.274557345 + 2.083333334 = 4.357890679 x = 4.357890679 Simplifying x = 4.357890679Subproblem 2
x + -2.083333334 = -2.274557345 Simplifying x + -2.083333334 = -2.274557345 Reorder the terms: -2.083333334 + x = -2.274557345 Solving -2.083333334 + x = -2.274557345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.083333334' to each side of the equation. -2.083333334 + 2.083333334 + x = -2.274557345 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -2.274557345 + 2.083333334 x = -2.274557345 + 2.083333334 Combine like terms: -2.274557345 + 2.083333334 = -0.191224011 x = -0.191224011 Simplifying x = -0.191224011Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.357890679, -0.191224011}
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