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Simplifying 6x(x + 4) = 4x + -10x + -8 Reorder the terms: 6x(4 + x) = 4x + -10x + -8 (4 * 6x + x * 6x) = 4x + -10x + -8 (24x + 6x2) = 4x + -10x + -8 Reorder the terms: 24x + 6x2 = -8 + 4x + -10x Combine like terms: 4x + -10x = -6x 24x + 6x2 = -8 + -6x Solving 24x + 6x2 = -8 + -6x Solving for variable 'x'. Reorder the terms: 8 + 24x + 6x + 6x2 = -8 + -6x + 8 + 6x Combine like terms: 24x + 6x = 30x 8 + 30x + 6x2 = -8 + -6x + 8 + 6x Reorder the terms: 8 + 30x + 6x2 = -8 + 8 + -6x + 6x Combine like terms: -8 + 8 = 0 8 + 30x + 6x2 = 0 + -6x + 6x 8 + 30x + 6x2 = -6x + 6x Combine like terms: -6x + 6x = 0 8 + 30x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(4 + 15x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + 15x + 3x2)' equal to zero and attempt to solve: Simplifying 4 + 15x + 3x2 = 0 Solving 4 + 15x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.333333333 + 5x + x2 = 0 Move the constant term to the right: Add '-1.333333333' to each side of the equation. 1.333333333 + 5x + -1.333333333 + x2 = 0 + -1.333333333 Reorder the terms: 1.333333333 + -1.333333333 + 5x + x2 = 0 + -1.333333333 Combine like terms: 1.333333333 + -1.333333333 = 0.000000000 0.000000000 + 5x + x2 = 0 + -1.333333333 5x + x2 = 0 + -1.333333333 Combine like terms: 0 + -1.333333333 = -1.333333333 5x + x2 = -1.333333333 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -1.333333333 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -1.333333333 + 6.25 Combine like terms: -1.333333333 + 6.25 = 4.916666667 6.25 + 5x + x2 = 4.916666667 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 4.916666667 Calculate the square root of the right side: 2.217355783 Break this problem into two subproblems by setting (x + 2.5) equal to 2.217355783 and -2.217355783.Subproblem 1
x + 2.5 = 2.217355783 Simplifying x + 2.5 = 2.217355783 Reorder the terms: 2.5 + x = 2.217355783 Solving 2.5 + x = 2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.217355783 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.217355783 + -2.5 x = 2.217355783 + -2.5 Combine like terms: 2.217355783 + -2.5 = -0.282644217 x = -0.282644217 Simplifying x = -0.282644217Subproblem 2
x + 2.5 = -2.217355783 Simplifying x + 2.5 = -2.217355783 Reorder the terms: 2.5 + x = -2.217355783 Solving 2.5 + x = -2.217355783 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.217355783 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.217355783 + -2.5 x = -2.217355783 + -2.5 Combine like terms: -2.217355783 + -2.5 = -4.717355783 x = -4.717355783 Simplifying x = -4.717355783Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.282644217, -4.717355783}Solution
x = {-0.282644217, -4.717355783}
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