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Simplifying -3x(x + -8) + 7x = 12 Reorder the terms: -3x(-8 + x) + 7x = 12 (-8 * -3x + x * -3x) + 7x = 12 (24x + -3x2) + 7x = 12 Reorder the terms: 24x + 7x + -3x2 = 12 Combine like terms: 24x + 7x = 31x 31x + -3x2 = 12 Solving 31x + -3x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + 31x + -3x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + 31x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4 + -10.33333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -10.33333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -10.33333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -10.33333333x + x2 = 0 + -4 -10.33333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -10.33333333x + x2 = -4 The x term is -10.33333333x. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x + 26.69444443 + x2 = -4 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x + x2 = -4 + 26.69444443 Combine like terms: -4 + 26.69444443 = 22.69444443 26.69444443 + -10.33333333x + x2 = 22.69444443 Factor a perfect square on the left side: (x + -5.166666665)(x + -5.166666665) = 22.69444443 Calculate the square root of the right side: 4.763868641 Break this problem into two subproblems by setting (x + -5.166666665) equal to 4.763868641 and -4.763868641.Subproblem 1
x + -5.166666665 = 4.763868641 Simplifying x + -5.166666665 = 4.763868641 Reorder the terms: -5.166666665 + x = 4.763868641 Solving -5.166666665 + x = 4.763868641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 4.763868641 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 4.763868641 + 5.166666665 x = 4.763868641 + 5.166666665 Combine like terms: 4.763868641 + 5.166666665 = 9.930535306 x = 9.930535306 Simplifying x = 9.930535306Subproblem 2
x + -5.166666665 = -4.763868641 Simplifying x + -5.166666665 = -4.763868641 Reorder the terms: -5.166666665 + x = -4.763868641 Solving -5.166666665 + x = -4.763868641 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -4.763868641 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -4.763868641 + 5.166666665 x = -4.763868641 + 5.166666665 Combine like terms: -4.763868641 + 5.166666665 = 0.402798024 x = 0.402798024 Simplifying x = 0.402798024Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.930535306, 0.402798024}
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