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Simplifying 3x + -2(x + 6) = 4x(x + -10) Reorder the terms: 3x + -2(6 + x) = 4x(x + -10) 3x + (6 * -2 + x * -2) = 4x(x + -10) 3x + (-12 + -2x) = 4x(x + -10) Reorder the terms: -12 + 3x + -2x = 4x(x + -10) Combine like terms: 3x + -2x = 1x -12 + 1x = 4x(x + -10) Reorder the terms: -12 + 1x = 4x(-10 + x) -12 + 1x = (-10 * 4x + x * 4x) -12 + 1x = (-40x + 4x2) Solving -12 + 1x = -40x + 4x2 Solving for variable 'x'. Combine like terms: 1x + 40x = 41x -12 + 41x + -4x2 = -40x + 4x2 + 40x + -4x2 Reorder the terms: -12 + 41x + -4x2 = -40x + 40x + 4x2 + -4x2 Combine like terms: -40x + 40x = 0 -12 + 41x + -4x2 = 0 + 4x2 + -4x2 -12 + 41x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12 + 41x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3 + -10.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -10.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -10.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -10.25x + x2 = 0 + -3 -10.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -10.25x + x2 = -3 The x term is -10.25x. Take half its coefficient (-5.125). Square it (26.265625) and add it to both sides. Add '26.265625' to each side of the equation. -10.25x + 26.265625 + x2 = -3 + 26.265625 Reorder the terms: 26.265625 + -10.25x + x2 = -3 + 26.265625 Combine like terms: -3 + 26.265625 = 23.265625 26.265625 + -10.25x + x2 = 23.265625 Factor a perfect square on the left side: (x + -5.125)(x + -5.125) = 23.265625 Calculate the square root of the right side: 4.823445345 Break this problem into two subproblems by setting (x + -5.125) equal to 4.823445345 and -4.823445345.Subproblem 1
x + -5.125 = 4.823445345 Simplifying x + -5.125 = 4.823445345 Reorder the terms: -5.125 + x = 4.823445345 Solving -5.125 + x = 4.823445345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = 4.823445345 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = 4.823445345 + 5.125 x = 4.823445345 + 5.125 Combine like terms: 4.823445345 + 5.125 = 9.948445345 x = 9.948445345 Simplifying x = 9.948445345Subproblem 2
x + -5.125 = -4.823445345 Simplifying x + -5.125 = -4.823445345 Reorder the terms: -5.125 + x = -4.823445345 Solving -5.125 + x = -4.823445345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.125' to each side of the equation. -5.125 + 5.125 + x = -4.823445345 + 5.125 Combine like terms: -5.125 + 5.125 = 0.000 0.000 + x = -4.823445345 + 5.125 x = -4.823445345 + 5.125 Combine like terms: -4.823445345 + 5.125 = 0.301554655 x = 0.301554655 Simplifying x = 0.301554655Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.948445345, 0.301554655}
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