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Simplifying 1.5x2 = 4.75x + -2.1 Reorder the terms: 1.5x2 = -2.1 + 4.75x Solving 1.5x2 = -2.1 + 4.75x Solving for variable 'x'. Reorder the terms: 2.1 + -4.75x + 1.5x2 = -2.1 + 4.75x + 2.1 + -4.75x Reorder the terms: 2.1 + -4.75x + 1.5x2 = -2.1 + 2.1 + 4.75x + -4.75x Combine like terms: -2.1 + 2.1 = 0.0 2.1 + -4.75x + 1.5x2 = 0.0 + 4.75x + -4.75x 2.1 + -4.75x + 1.5x2 = 4.75x + -4.75x Combine like terms: 4.75x + -4.75x = 0.00 2.1 + -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'. 1.4 + -3.166666667x + x2 = 0.0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -3.166666667x + -1.4 + x2 = 0.0 + -1.4 Reorder the terms: 1.4 + -1.4 + -3.166666667x + x2 = 0.0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -3.166666667x + x2 = 0.0 + -1.4 -3.166666667x + x2 = 0.0 + -1.4 Combine like terms: 0.0 + -1.4 = -1.4 -3.166666667x + x2 = -1.4 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 = -1.4 + 2.506944447 Reorder the terms: 2.506944447 + -3.166666667x + x2 = -1.4 + 2.506944447 Combine like terms: -1.4 + 2.506944447 = 1.106944447 2.506944447 + -3.166666667x + x2 = 1.106944447 Factor a perfect square on the left side: (x + -1.583333334)(x + -1.583333334) = 1.106944447 Calculate the square root of the right side: 1.052114275 Break this problem into two subproblems by setting (x + -1.583333334) equal to 1.052114275 and -1.052114275.Subproblem 1
x + -1.583333334 = 1.052114275 Simplifying x + -1.583333334 = 1.052114275 Reorder the terms: -1.583333334 + x = 1.052114275 Solving -1.583333334 + x = 1.052114275 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 = 1.052114275 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = 1.052114275 + 1.583333334 x = 1.052114275 + 1.583333334 Combine like terms: 1.052114275 + 1.583333334 = 2.635447609 x = 2.635447609 Simplifying x = 2.635447609Subproblem 2
x + -1.583333334 = -1.052114275 Simplifying x + -1.583333334 = -1.052114275 Reorder the terms: -1.583333334 + x = -1.052114275 Solving -1.583333334 + x = -1.052114275 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 = -1.052114275 + 1.583333334 Combine like terms: -1.583333334 + 1.583333334 = 0.000000000 0.000000000 + x = -1.052114275 + 1.583333334 x = -1.052114275 + 1.583333334 Combine like terms: -1.052114275 + 1.583333334 = 0.531219059 x = 0.531219059 Simplifying x = 0.531219059Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.635447609, 0.531219059}
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