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Simplifying -3x(x + 5) = 8x + 18 Reorder the terms: -3x(5 + x) = 8x + 18 (5 * -3x + x * -3x) = 8x + 18 (-15x + -3x2) = 8x + 18 Reorder the terms: -15x + -3x2 = 18 + 8x Solving -15x + -3x2 = 18 + 8x Solving for variable 'x'. Reorder the terms: -18 + -15x + -8x + -3x2 = 18 + 8x + -18 + -8x Combine like terms: -15x + -8x = -23x -18 + -23x + -3x2 = 18 + 8x + -18 + -8x Reorder the terms: -18 + -23x + -3x2 = 18 + -18 + 8x + -8x Combine like terms: 18 + -18 = 0 -18 + -23x + -3x2 = 0 + 8x + -8x -18 + -23x + -3x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -18 + -23x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 23x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + 23x + 3x2)' equal to zero and attempt to solve: Simplifying 18 + 23x + 3x2 = 0 Solving 18 + 23x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 6 + 7.666666667x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 7.666666667x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 7.666666667x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 7.666666667x + x2 = 0 + -6 7.666666667x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 7.666666667x + x2 = -6 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 = -6 + 14.69444445 Reorder the terms: 14.69444445 + 7.666666667x + x2 = -6 + 14.69444445 Combine like terms: -6 + 14.69444445 = 8.69444445 14.69444445 + 7.666666667x + x2 = 8.69444445 Factor a perfect square on the left side: (x + 3.833333334)(x + 3.833333334) = 8.69444445 Calculate the square root of the right side: 2.948634336 Break this problem into two subproblems by setting (x + 3.833333334) equal to 2.948634336 and -2.948634336.Subproblem 1
x + 3.833333334 = 2.948634336 Simplifying x + 3.833333334 = 2.948634336 Reorder the terms: 3.833333334 + x = 2.948634336 Solving 3.833333334 + x = 2.948634336 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 = 2.948634336 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = 2.948634336 + -3.833333334 x = 2.948634336 + -3.833333334 Combine like terms: 2.948634336 + -3.833333334 = -0.884698998 x = -0.884698998 Simplifying x = -0.884698998Subproblem 2
x + 3.833333334 = -2.948634336 Simplifying x + 3.833333334 = -2.948634336 Reorder the terms: 3.833333334 + x = -2.948634336 Solving 3.833333334 + x = -2.948634336 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 = -2.948634336 + -3.833333334 Combine like terms: 3.833333334 + -3.833333334 = 0.000000000 0.000000000 + x = -2.948634336 + -3.833333334 x = -2.948634336 + -3.833333334 Combine like terms: -2.948634336 + -3.833333334 = -6.78196767 x = -6.78196767 Simplifying x = -6.78196767Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.884698998, -6.78196767}Solution
x = {-0.884698998, -6.78196767}
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