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Simplifying 1.5x2 = 4.75x + -2.3 Reorder the terms: 1.5x2 = -2.3 + 4.75x Solving 1.5x2 = -2.3 + 4.75x Solving for variable 'x'. Reorder the terms: 2.3 + -4.75x + 1.5x2 = -2.3 + 4.75x + 2.3 + -4.75x Reorder the terms: 2.3 + -4.75x + 1.5x2 = -2.3 + 2.3 + 4.75x + -4.75x Combine like terms: -2.3 + 2.3 = 0.0 2.3 + -4.75x + 1.5x2 = 0.0 + 4.75x + -4.75x 2.3 + -4.75x + 1.5x2 = 4.75x + -4.75x Combine like terms: 4.75x + -4.75x = 0.00 2.3 + -4.75x + 1.5x2 = 0.00 Begin completing the square. Divide all terms by 1.5 the coefficient of the squared term: Divide each side by '1.5'. 1.533333333 + -3.166666667x + x2 = 0.0 Move the constant term to the right: Add '-1.533333333' to each side of the equation. 1.533333333 + -3.166666667x + -1.533333333 + x2 = 0.0 + -1.533333333 Reorder the terms: 1.533333333 + -1.533333333 + -3.166666667x + x2 = 0.0 + -1.533333333 Combine like terms: 1.533333333 + -1.533333333 = 0.000000000 0.000000000 + -3.166666667x + x2 = 0.0 + -1.533333333 -3.166666667x + x2 = 0.0 + -1.533333333 Combine like terms: 0.0 + -1.533333333 = -1.533333333 -3.166666667x + x2 = -1.533333333 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 = -1.533333333 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.533333333 + 2.506944447 Combine like terms: -1.533333333 + 2.506944447 = 0.973611114 2.506944447 + -3.166666667x + x2 = 0.973611114 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 0.973611114 Calculate the square root of the right side: 0.986717343 Break this problem into two subproblems by setting (x + -1.583333334) equal to 0.986717343 and -0.986717343.Subproblem 1
x + -1.583333334 = 0.986717343 Simplifying x + -1.583333334 = 0.986717343 Reorder the terms: -1.583333334 + x = 0.986717343 Solving -1.583333334 + x = 0.986717343 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 = 0.986717343 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 0.986717343 + 1.583333334 x = 0.986717343 + 1.583333334 Combine like terms: 0.986717343 + 1.583333334 = 2.570050677 x = 2.570050677 Simplifying x = 2.570050677Subproblem 2
x + -1.583333334 = -0.986717343 Simplifying x + -1.583333334 = -0.986717343 Reorder the terms: -1.583333334 + x = -0.986717343 Solving -1.583333334 + x = -0.986717343 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 = -0.986717343 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -0.986717343 + 1.583333334 x = -0.986717343 + 1.583333334 Combine like terms: -0.986717343 + 1.583333334 = 0.596615991 x = 0.596615991 Simplifying x = 0.596615991Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.570050677, 0.596615991}
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