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Simplifying 5x(6x + 4) + 4 = 16 Reorder the terms: 5x(4 + 6x) + 4 = 16 (4 * 5x + 6x * 5x) + 4 = 16 (20x + 30x2) + 4 = 16 Reorder the terms: 4 + 20x + 30x2 = 16 Solving 4 + 20x + 30x2 = 16 Solving for variable 'x'. Reorder the terms: 4 + -16 + 20x + 30x2 = 16 + -16 Combine like terms: 4 + -16 = -12 -12 + 20x + 30x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -12 + 20x + 30x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 10x + 15x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 10x + 15x2)' equal to zero and attempt to solve: Simplifying -6 + 10x + 15x2 = 0 Solving -6 + 10x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -0.4 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '0.4' to each side of the equation. -0.4 + 0.6666666667x + 0.4 + x2 = 0 + 0.4 Reorder the terms: -0.4 + 0.4 + 0.6666666667x + x2 = 0 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + 0.6666666667x + x2 = 0 + 0.4 0.6666666667x + x2 = 0 + 0.4 Combine like terms: 0 + 0.4 = 0.4 0.6666666667x + x2 = 0.4 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = 0.4 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = 0.4 + 0.1111111112 Combine like terms: 0.4 + 0.1111111112 = 0.5111111112 0.1111111112 + 0.6666666667x + x2 = 0.5111111112 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = 0.5111111112 Calculate the square root of the right side: 0.714920353 Break this problem into two subproblems by setting (x + 0.3333333334) equal to 0.714920353 and -0.714920353.Subproblem 1
x + 0.3333333334 = 0.714920353 Simplifying x + 0.3333333334 = 0.714920353 Reorder the terms: 0.3333333334 + x = 0.714920353 Solving 0.3333333334 + x = 0.714920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = 0.714920353 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = 0.714920353 + -0.3333333334 x = 0.714920353 + -0.3333333334 Combine like terms: 0.714920353 + -0.3333333334 = 0.3815870196 x = 0.3815870196 Simplifying x = 0.3815870196Subproblem 2
x + 0.3333333334 = -0.714920353 Simplifying x + 0.3333333334 = -0.714920353 Reorder the terms: 0.3333333334 + x = -0.714920353 Solving 0.3333333334 + x = -0.714920353 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3333333334' to each side of the equation. 0.3333333334 + -0.3333333334 + x = -0.714920353 + -0.3333333334 Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000 0.0000000000 + x = -0.714920353 + -0.3333333334 x = -0.714920353 + -0.3333333334 Combine like terms: -0.714920353 + -0.3333333334 = -1.0482536864 x = -1.0482536864 Simplifying x = -1.0482536864Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3815870196, -1.0482536864}Solution
x = {0.3815870196, -1.0482536864}
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