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Simplifying 7x + 3 = 6x(x + -2) Reorder the terms: 3 + 7x = 6x(x + -2) Reorder the terms: 3 + 7x = 6x(-2 + x) 3 + 7x = (-2 * 6x + x * 6x) 3 + 7x = (-12x + 6x2) Solving 3 + 7x = -12x + 6x2 Solving for variable 'x'. Combine like terms: 7x + 12x = 19x 3 + 19x + -6x2 = -12x + 6x2 + 12x + -6x2 Reorder the terms: 3 + 19x + -6x2 = -12x + 12x + 6x2 + -6x2 Combine like terms: -12x + 12x = 0 3 + 19x + -6x2 = 0 + 6x2 + -6x2 3 + 19x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 3 + 19x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. -0.5 + -3.166666667x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.166666667x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.166666667x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.166666667x + x2 = 0 + 0.5 -3.166666667x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.166666667x + x2 = 0.5 The x term is -3.166666667x. Take half its coefficient (-1.583333334). Square it (2.506944447) and add it to both sides. Add '2.506944447' to each side of the equation. -3.166666667x + 2.506944447 + x2 = 0.5 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = 0.5 + 2.506944447 Combine like terms: 0.5 + 2.506944447 = 3.006944447 2.506944447 + -3.166666667x + x2 = 3.006944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 3.006944447 Calculate the square root of the right side: 1.734054338 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.734054338 and -1.734054338.Subproblem 1
x + -1.583333334 = 1.734054338 Simplifying x + -1.583333334 = 1.734054338 Reorder the terms: -1.583333334 + x = 1.734054338 Solving -1.583333334 + x = 1.734054338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = 1.734054338 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.734054338 + 1.583333334 x = 1.734054338 + 1.583333334 Combine like terms: 1.734054338 + 1.583333334 = 3.317387672 x = 3.317387672 Simplifying x = 3.317387672Subproblem 2
x + -1.583333334 = -1.734054338 Simplifying x + -1.583333334 = -1.734054338 Reorder the terms: -1.583333334 + x = -1.734054338 Solving -1.583333334 + x = -1.734054338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.583333334' to each side of the equation. -1.583333334 + 1.583333334 + x = -1.734054338 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.734054338 + 1.583333334 x = -1.734054338 + 1.583333334 Combine like terms: -1.734054338 + 1.583333334 = -0.150721004 x = -0.150721004 Simplifying x = -0.150721004Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.317387672, -0.150721004}
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