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Simplifying -3x(x + 5) = -3x + 5 Reorder the terms: -3x(5 + x) = -3x + 5 (5 * -3x + x * -3x) = -3x + 5 (-15x + -3x2) = -3x + 5 Reorder the terms: -15x + -3x2 = 5 + -3x Solving -15x + -3x2 = 5 + -3x Solving for variable 'x'. Reorder the terms: -5 + -15x + 3x + -3x2 = 5 + -3x + -5 + 3x Combine like terms: -15x + 3x = -12x -5 + -12x + -3x2 = 5 + -3x + -5 + 3x Reorder the terms: -5 + -12x + -3x2 = 5 + -5 + -3x + 3x Combine like terms: 5 + -5 = 0 -5 + -12x + -3x2 = 0 + -3x + 3x -5 + -12x + -3x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -5 + -12x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 12x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 12x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 12x + 3x2 = 0 Solving 5 + 12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 4x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 4x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 4x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 4x + x2 = 0 + -1.666666667 4x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 4x + x2 = -1.666666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -1.666666667 + 4 Reorder the terms: 4 + 4x + x2 = -1.666666667 + 4 Combine like terms: -1.666666667 + 4 = 2.333333333 4 + 4x + x2 = 2.333333333 Factor a perfect square on the left side: (x + 2)(x + 2) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + 2) equal to 1.527525232 and -1.527525232.Subproblem 1
x + 2 = 1.527525232 Simplifying x + 2 = 1.527525232 Reorder the terms: 2 + x = 1.527525232 Solving 2 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.527525232 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.527525232 + -2 x = 1.527525232 + -2 Combine like terms: 1.527525232 + -2 = -0.472474768 x = -0.472474768 Simplifying x = -0.472474768Subproblem 2
x + 2 = -1.527525232 Simplifying x + 2 = -1.527525232 Reorder the terms: 2 + x = -1.527525232 Solving 2 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.527525232 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.527525232 + -2 x = -1.527525232 + -2 Combine like terms: -1.527525232 + -2 = -3.527525232 x = -3.527525232 Simplifying x = -3.527525232Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.472474768, -3.527525232}Solution
x = {-0.472474768, -3.527525232}
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