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Simplifying (10x + -25)(-6x + 28) = 6x + -17 Reorder the terms: (-25 + 10x)(-6x + 28) = 6x + -17 Reorder the terms: (-25 + 10x)(28 + -6x) = 6x + -17 Multiply (-25 + 10x) * (28 + -6x) (-25(28 + -6x) + 10x * (28 + -6x)) = 6x + -17 ((28 * -25 + -6x * -25) + 10x * (28 + -6x)) = 6x + -17 ((-700 + 150x) + 10x * (28 + -6x)) = 6x + -17 (-700 + 150x + (28 * 10x + -6x * 10x)) = 6x + -17 (-700 + 150x + (280x + -60x2)) = 6x + -17 Combine like terms: 150x + 280x = 430x (-700 + 430x + -60x2) = 6x + -17 Reorder the terms: -700 + 430x + -60x2 = -17 + 6x Solving -700 + 430x + -60x2 = -17 + 6x Solving for variable 'x'. Reorder the terms: -700 + 17 + 430x + -6x + -60x2 = -17 + 6x + 17 + -6x Combine like terms: -700 + 17 = -683 -683 + 430x + -6x + -60x2 = -17 + 6x + 17 + -6x Combine like terms: 430x + -6x = 424x -683 + 424x + -60x2 = -17 + 6x + 17 + -6x Reorder the terms: -683 + 424x + -60x2 = -17 + 17 + 6x + -6x Combine like terms: -17 + 17 = 0 -683 + 424x + -60x2 = 0 + 6x + -6x -683 + 424x + -60x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -683 + 424x + -60x2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. 11.38333333 + -7.066666667x + x2 = 0.0 Move the constant term to the right: Add '-11.38333333' to each side of the equation. 11.38333333 + -7.066666667x + -11.38333333 + x2 = 0.0 + -11.38333333 Reorder the terms: 11.38333333 + -11.38333333 + -7.066666667x + x2 = 0.0 + -11.38333333 Combine like terms: 11.38333333 + -11.38333333 = 0.00000000 0.00000000 + -7.066666667x + x2 = 0.0 + -11.38333333 -7.066666667x + x2 = 0.0 + -11.38333333 Combine like terms: 0.0 + -11.38333333 = -11.38333333 -7.066666667x + x2 = -11.38333333 The x term is -7.066666667x. Take half its coefficient (-3.533333334). Square it (12.48444445) and add it to both sides. Add '12.48444445' to each side of the equation. -7.066666667x + 12.48444445 + x2 = -11.38333333 + 12.48444445 Reorder the terms: 12.48444445 + -7.066666667x + x2 = -11.38333333 + 12.48444445 Combine like terms: -11.38333333 + 12.48444445 = 1.10111112 12.48444445 + -7.066666667x + x2 = 1.10111112 Factor a perfect square on the left side: (x + -3.533333334)(x + -3.533333334) = 1.10111112 Calculate the square root of the right side: 1.04933842 Break this problem into two subproblems by setting (x + -3.533333334) equal to 1.04933842 and -1.04933842.Subproblem 1
x + -3.533333334 = 1.04933842 Simplifying x + -3.533333334 = 1.04933842 Reorder the terms: -3.533333334 + x = 1.04933842 Solving -3.533333334 + x = 1.04933842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.533333334' to each side of the equation. -3.533333334 + 3.533333334 + x = 1.04933842 + 3.533333334 Combine like terms: -3.533333334 + 3.533333334 = 0.000000000 0.000000000 + x = 1.04933842 + 3.533333334 x = 1.04933842 + 3.533333334 Combine like terms: 1.04933842 + 3.533333334 = 4.582671754 x = 4.582671754 Simplifying x = 4.582671754Subproblem 2
x + -3.533333334 = -1.04933842 Simplifying x + -3.533333334 = -1.04933842 Reorder the terms: -3.533333334 + x = -1.04933842 Solving -3.533333334 + x = -1.04933842 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.533333334' to each side of the equation. -3.533333334 + 3.533333334 + x = -1.04933842 + 3.533333334 Combine like terms: -3.533333334 + 3.533333334 = 0.000000000 0.000000000 + x = -1.04933842 + 3.533333334 x = -1.04933842 + 3.533333334 Combine like terms: -1.04933842 + 3.533333334 = 2.483994914 x = 2.483994914 Simplifying x = 2.483994914Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.582671754, 2.483994914}
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