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Simplifying 6x + -10 = 3x(x + -5) + -8 Reorder the terms: -10 + 6x = 3x(x + -5) + -8 Reorder the terms: -10 + 6x = 3x(-5 + x) + -8 -10 + 6x = (-5 * 3x + x * 3x) + -8 -10 + 6x = (-15x + 3x2) + -8 Reorder the terms: -10 + 6x = -8 + -15x + 3x2 Solving -10 + 6x = -8 + -15x + 3x2 Solving for variable 'x'. Reorder the terms: -10 + 8 + 6x + 15x + -3x2 = -8 + -15x + 3x2 + 8 + 15x + -3x2 Combine like terms: -10 + 8 = -2 -2 + 6x + 15x + -3x2 = -8 + -15x + 3x2 + 8 + 15x + -3x2 Combine like terms: 6x + 15x = 21x -2 + 21x + -3x2 = -8 + -15x + 3x2 + 8 + 15x + -3x2 Reorder the terms: -2 + 21x + -3x2 = -8 + 8 + -15x + 15x + 3x2 + -3x2 Combine like terms: -8 + 8 = 0 -2 + 21x + -3x2 = 0 + -15x + 15x + 3x2 + -3x2 -2 + 21x + -3x2 = -15x + 15x + 3x2 + -3x2 Combine like terms: -15x + 15x = 0 -2 + 21x + -3x2 = 0 + 3x2 + -3x2 -2 + 21x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -2 + 21x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 0.6666666667 + -7x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -7x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -7x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -7x + x2 = 0 + -0.6666666667 -7x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -7x + x2 = -0.6666666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -0.6666666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -0.6666666667 + 12.25 Combine like terms: -0.6666666667 + 12.25 = 11.5833333333 12.25 + -7x + x2 = 11.5833333333 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 11.5833333333 Calculate the square root of the right side: 3.403429643 Break this problem into two subproblems by setting (x + -3.5) equal to 3.403429643 and -3.403429643.Subproblem 1
x + -3.5 = 3.403429643 Simplifying x + -3.5 = 3.403429643 Reorder the terms: -3.5 + x = 3.403429643 Solving -3.5 + x = 3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.403429643 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.403429643 + 3.5 x = 3.403429643 + 3.5 Combine like terms: 3.403429643 + 3.5 = 6.903429643 x = 6.903429643 Simplifying x = 6.903429643Subproblem 2
x + -3.5 = -3.403429643 Simplifying x + -3.5 = -3.403429643 Reorder the terms: -3.5 + x = -3.403429643 Solving -3.5 + x = -3.403429643 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.403429643 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.403429643 + 3.5 x = -3.403429643 + 3.5 Combine like terms: -3.403429643 + 3.5 = 0.096570357 x = 0.096570357 Simplifying x = 0.096570357Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.903429643, 0.096570357}
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