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Simplifying 3x(2x + -7) = 4x + -7 Reorder the terms: 3x(-7 + 2x) = 4x + -7 (-7 * 3x + 2x * 3x) = 4x + -7 (-21x + 6x2) = 4x + -7 Reorder the terms: -21x + 6x2 = -7 + 4x Solving -21x + 6x2 = -7 + 4x Solving for variable 'x'. Reorder the terms: 7 + -21x + -4x + 6x2 = -7 + 4x + 7 + -4x Combine like terms: -21x + -4x = -25x 7 + -25x + 6x2 = -7 + 4x + 7 + -4x Reorder the terms: 7 + -25x + 6x2 = -7 + 7 + 4x + -4x Combine like terms: -7 + 7 = 0 7 + -25x + 6x2 = 0 + 4x + -4x 7 + -25x + 6x2 = 4x + -4x Combine like terms: 4x + -4x = 0 7 + -25x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. 1.166666667 + -4.166666667x + x2 = 0 Move the constant term to the right: Add '-1.166666667' to each side of the equation. 1.166666667 + -4.166666667x + -1.166666667 + x2 = 0 + -1.166666667 Reorder the terms: 1.166666667 + -1.166666667 + -4.166666667x + x2 = 0 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + -4.166666667x + x2 = 0 + -1.166666667 -4.166666667x + x2 = 0 + -1.166666667 Combine like terms: 0 + -1.166666667 = -1.166666667 -4.166666667x + x2 = -1.166666667 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 = -1.166666667 + 4.340277781 Reorder the terms: 4.340277781 + -4.166666667x + x2 = -1.166666667 + 4.340277781 Combine like terms: -1.166666667 + 4.340277781 = 3.173611114 4.340277781 + -4.166666667x + x2 = 3.173611114 Factor a perfect square on the left side: (x + -2.083333334)(x + -2.083333334) = 3.173611114 Calculate the square root of the right side: 1.781463195 Break this problem into two subproblems by setting (x + -2.083333334) equal to 1.781463195 and -1.781463195.Subproblem 1
x + -2.083333334 = 1.781463195 Simplifying x + -2.083333334 = 1.781463195 Reorder the terms: -2.083333334 + x = 1.781463195 Solving -2.083333334 + x = 1.781463195 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 = 1.781463195 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = 1.781463195 + 2.083333334 x = 1.781463195 + 2.083333334 Combine like terms: 1.781463195 + 2.083333334 = 3.864796529 x = 3.864796529 Simplifying x = 3.864796529Subproblem 2
x + -2.083333334 = -1.781463195 Simplifying x + -2.083333334 = -1.781463195 Reorder the terms: -2.083333334 + x = -1.781463195 Solving -2.083333334 + x = -1.781463195 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 = -1.781463195 + 2.083333334 Combine like terms: -2.083333334 + 2.083333334 = 0.000000000 0.000000000 + x = -1.781463195 + 2.083333334 x = -1.781463195 + 2.083333334 Combine like terms: -1.781463195 + 2.083333334 = 0.301870139 x = 0.301870139 Simplifying x = 0.301870139Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.864796529, 0.301870139}
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