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Simplifying 6x2 + -43x = 75 Reorder the terms: -43x + 6x2 = 75 Solving -43x + 6x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + -43x + 6x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + -43x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -12.5 + -7.166666667x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -7.166666667x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -7.166666667x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -7.166666667x + x2 = 0 + 12.5 -7.166666667x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -7.166666667x + x2 = 12.5 The x term is -7.166666667x. Take half its coefficient (-3.583333334). Square it (12.84027778) and add it to both sides. Add '12.84027778' to each side of the equation. -7.166666667x + 12.84027778 + x2 = 12.5 + 12.84027778 Reorder the terms: 12.84027778 + -7.166666667x + x2 = 12.5 + 12.84027778 Combine like terms: 12.5 + 12.84027778 = 25.34027778 12.84027778 + -7.166666667x + x2 = 25.34027778 Factor a perfect square on the left side: (x + -3.583333334)(x + -3.583333334) = 25.34027778 Calculate the square root of the right side: 5.03391277 Break this problem into two subproblems by setting (x + -3.583333334) equal to 5.03391277 and -5.03391277.Subproblem 1
x + -3.583333334 = 5.03391277 Simplifying x + -3.583333334 = 5.03391277 Reorder the terms: -3.583333334 + x = 5.03391277 Solving -3.583333334 + x = 5.03391277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = 5.03391277 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = 5.03391277 + 3.583333334 x = 5.03391277 + 3.583333334 Combine like terms: 5.03391277 + 3.583333334 = 8.617246104 x = 8.617246104 Simplifying x = 8.617246104Subproblem 2
x + -3.583333334 = -5.03391277 Simplifying x + -3.583333334 = -5.03391277 Reorder the terms: -3.583333334 + x = -5.03391277 Solving -3.583333334 + x = -5.03391277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.583333334' to each side of the equation. -3.583333334 + 3.583333334 + x = -5.03391277 + 3.583333334 Combine like terms: -3.583333334 + 3.583333334 = 0.000000000 0.000000000 + x = -5.03391277 + 3.583333334 x = -5.03391277 + 3.583333334 Combine like terms: -5.03391277 + 3.583333334 = -1.450579436 x = -1.450579436 Simplifying x = -1.450579436Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.617246104, -1.450579436}
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