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Simplifying 4x(x + -6) + -5x(2x + 3) = -6 Reorder the terms: 4x(-6 + x) + -5x(2x + 3) = -6 (-6 * 4x + x * 4x) + -5x(2x + 3) = -6 (-24x + 4x2) + -5x(2x + 3) = -6 Reorder the terms: -24x + 4x2 + -5x(3 + 2x) = -6 -24x + 4x2 + (3 * -5x + 2x * -5x) = -6 -24x + 4x2 + (-15x + -10x2) = -6 Reorder the terms: -24x + -15x + 4x2 + -10x2 = -6 Combine like terms: -24x + -15x = -39x -39x + 4x2 + -10x2 = -6 Combine like terms: 4x2 + -10x2 = -6x2 -39x + -6x2 = -6 Solving -39x + -6x2 = -6 Solving for variable 'x'. Reorder the terms: 6 + -39x + -6x2 = -6 + 6 Combine like terms: -6 + 6 = 0 6 + -39x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(2 + -13x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -13x + -2x2)' equal to zero and attempt to solve: Simplifying 2 + -13x + -2x2 = 0 Solving 2 + -13x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -1 + 6.5x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 6.5x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 6.5x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 6.5x + x2 = 0 + 1 6.5x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 6.5x + x2 = 1 The x term is 6.5x. Take half its coefficient (3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. 6.5x + 10.5625 + x2 = 1 + 10.5625 Reorder the terms: 10.5625 + 6.5x + x2 = 1 + 10.5625 Combine like terms: 1 + 10.5625 = 11.5625 10.5625 + 6.5x + x2 = 11.5625 Factor a perfect square on the left side: (x + 3.25)(x + 3.25) = 11.5625 Calculate the square root of the right side: 3.400367627 Break this problem into two subproblems by setting (x + 3.25) equal to 3.400367627 and -3.400367627.Subproblem 1
x + 3.25 = 3.400367627 Simplifying x + 3.25 = 3.400367627 Reorder the terms: 3.25 + x = 3.400367627 Solving 3.25 + x = 3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = 3.400367627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = 3.400367627 + -3.25 x = 3.400367627 + -3.25 Combine like terms: 3.400367627 + -3.25 = 0.150367627 x = 0.150367627 Simplifying x = 0.150367627Subproblem 2
x + 3.25 = -3.400367627 Simplifying x + 3.25 = -3.400367627 Reorder the terms: 3.25 + x = -3.400367627 Solving 3.25 + x = -3.400367627 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.25' to each side of the equation. 3.25 + -3.25 + x = -3.400367627 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + x = -3.400367627 + -3.25 x = -3.400367627 + -3.25 Combine like terms: -3.400367627 + -3.25 = -6.650367627 x = -6.650367627 Simplifying x = -6.650367627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.150367627, -6.650367627}Solution
x = {0.150367627, -6.650367627}
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