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Simplifying (4x + 5) * x(6x + -2) = 9x Reorder the terms: (5 + 4x) * x(6x + -2) = 9x Reorder the terms: (5 + 4x) * x(-2 + 6x) = 9x Reorder the terms for easier multiplication: x(5 + 4x)(-2 + 6x) = 9x Multiply (5 + 4x) * (-2 + 6x) x(5(-2 + 6x) + 4x * (-2 + 6x)) = 9x x((-2 * 5 + 6x * 5) + 4x * (-2 + 6x)) = 9x x((-10 + 30x) + 4x * (-2 + 6x)) = 9x x(-10 + 30x + (-2 * 4x + 6x * 4x)) = 9x x(-10 + 30x + (-8x + 24x2)) = 9x Combine like terms: 30x + -8x = 22x x(-10 + 22x + 24x2) = 9x (-10 * x + 22x * x + 24x2 * x) = 9x (-10x + 22x2 + 24x3) = 9x Solving -10x + 22x2 + 24x3 = 9x Solving for variable 'x'. Reorder the terms: -10x + -9x + 22x2 + 24x3 = 9x + -9x Combine like terms: -10x + -9x = -19x -19x + 22x2 + 24x3 = 9x + -9x Combine like terms: 9x + -9x = 0 -19x + 22x2 + 24x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-19 + 22x + 24x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-19 + 22x + 24x2)' equal to zero and attempt to solve: Simplifying -19 + 22x + 24x2 = 0 Solving -19 + 22x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.7916666667 + 0.9166666667x + x2 = 0 Move the constant term to the right: Add '0.7916666667' to each side of the equation. -0.7916666667 + 0.9166666667x + 0.7916666667 + x2 = 0 + 0.7916666667 Reorder the terms: -0.7916666667 + 0.7916666667 + 0.9166666667x + x2 = 0 + 0.7916666667 Combine like terms: -0.7916666667 + 0.7916666667 = 0.0000000000 0.0000000000 + 0.9166666667x + x2 = 0 + 0.7916666667 0.9166666667x + x2 = 0 + 0.7916666667 Combine like terms: 0 + 0.7916666667 = 0.7916666667 0.9166666667x + x2 = 0.7916666667 The x term is 0.9166666667x. Take half its coefficient (0.4583333334). Square it (0.2100694445) and add it to both sides. Add '0.2100694445' to each side of the equation. 0.9166666667x + 0.2100694445 + x2 = 0.7916666667 + 0.2100694445 Reorder the terms: 0.2100694445 + 0.9166666667x + x2 = 0.7916666667 + 0.2100694445 Combine like terms: 0.7916666667 + 0.2100694445 = 1.0017361112 0.2100694445 + 0.9166666667x + x2 = 1.0017361112 Factor a perfect square on the left side: (x + 0.4583333334)(x + 0.4583333334) = 1.0017361112 Calculate the square root of the right side: 1.000867679 Break this problem into two subproblems by setting (x + 0.4583333334) equal to 1.000867679 and -1.000867679.Subproblem 1
x + 0.4583333334 = 1.000867679 Simplifying x + 0.4583333334 = 1.000867679 Reorder the terms: 0.4583333334 + x = 1.000867679 Solving 0.4583333334 + x = 1.000867679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = 1.000867679 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = 1.000867679 + -0.4583333334 x = 1.000867679 + -0.4583333334 Combine like terms: 1.000867679 + -0.4583333334 = 0.5425343456 x = 0.5425343456 Simplifying x = 0.5425343456Subproblem 2
x + 0.4583333334 = -1.000867679 Simplifying x + 0.4583333334 = -1.000867679 Reorder the terms: 0.4583333334 + x = -1.000867679 Solving 0.4583333334 + x = -1.000867679 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4583333334' to each side of the equation. 0.4583333334 + -0.4583333334 + x = -1.000867679 + -0.4583333334 Combine like terms: 0.4583333334 + -0.4583333334 = 0.0000000000 0.0000000000 + x = -1.000867679 + -0.4583333334 x = -1.000867679 + -0.4583333334 Combine like terms: -1.000867679 + -0.4583333334 = -1.4592010124 x = -1.4592010124 Simplifying x = -1.4592010124Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5425343456, -1.4592010124}Solution
x = {0, 0.5425343456, -1.4592010124}
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