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Simplifying 5x + -3[(x + -1)(x + -5)] = 0 Reorder the terms: 5x + -3[(-1 + x)(x + -5)] = 0 Reorder the terms: 5x + -3[(-1 + x)(-5 + x)] = 0 Multiply (-1 + x) * (-5 + x) 5x + -3[(-1(-5 + x) + x(-5 + x))] = 0 5x + -3[((-5 * -1 + x * -1) + x(-5 + x))] = 0 5x + -3[((5 + -1x) + x(-5 + x))] = 0 5x + -3[(5 + -1x + (-5 * x + x * x))] = 0 5x + -3[(5 + -1x + (-5x + x2))] = 0 Combine like terms: -1x + -5x = -6x 5x + -3[(5 + -6x + x2)] = 0 5x + [5 * -3 + -6x * -3 + x2 * -3] = 0 5x + [-15 + 18x + -3x2] = 0 Reorder the terms: -15 + 5x + 18x + -3x2 = 0 Combine like terms: 5x + 18x = 23x -15 + 23x + -3x2 = 0 Solving -15 + 23x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 5 + -7.666666667x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -7.666666667x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -7.666666667x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -7.666666667x + x2 = 0 + -5 -7.666666667x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -7.666666667x + x2 = -5 The x term is -7.666666667x. Take half its coefficient (-3.833333334). Square it (14.69444445) and add it to both sides. Add '14.69444445' to each side of the equation. -7.666666667x + 14.69444445 + x2 = -5 + 14.69444445 Reorder the terms: 14.69444445 + -7.666666667x + x2 = -5 + 14.69444445 Combine like terms: -5 + 14.69444445 = 9.69444445 14.69444445 + -7.666666667x + x2 = 9.69444445 Factor a perfect square on the left side: (x + -3.833333334)(x + -3.833333334) = 9.69444445 Calculate the square root of the right side: 3.113590283 Break this problem into two subproblems by setting (x + -3.833333334) equal to 3.113590283 and -3.113590283.Subproblem 1
x + -3.833333334 = 3.113590283 Simplifying x + -3.833333334 = 3.113590283 Reorder the terms: -3.833333334 + x = 3.113590283 Solving -3.833333334 + x = 3.113590283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = 3.113590283 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = 3.113590283 + 3.833333334 x = 3.113590283 + 3.833333334 Combine like terms: 3.113590283 + 3.833333334 = 6.946923617 x = 6.946923617 Simplifying x = 6.946923617Subproblem 2
x + -3.833333334 = -3.113590283 Simplifying x + -3.833333334 = -3.113590283 Reorder the terms: -3.833333334 + x = -3.113590283 Solving -3.833333334 + x = -3.113590283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.833333334' to each side of the equation. -3.833333334 + 3.833333334 + x = -3.113590283 + 3.833333334 Combine like terms: -3.833333334 + 3.833333334 = 0.000000000 0.000000000 + x = -3.113590283 + 3.833333334 x = -3.113590283 + 3.833333334 Combine like terms: -3.113590283 + 3.833333334 = 0.719743051 x = 0.719743051 Simplifying x = 0.719743051Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.946923617, 0.719743051}
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