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Simplifying 4x(3x + -5) = 16 Reorder the terms: 4x(-5 + 3x) = 16 (-5 * 4x + 3x * 4x) = 16 (-20x + 12x2) = 16 Solving -20x + 12x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -20x + 12x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -20x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-4 + -5x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-4 + -5x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + -5x + 3x2 = 0 Solving -4 + -5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -1.666666667x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.666666667x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.666666667x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.666666667x + x2 = 0 + 1.333333333 -1.666666667x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.666666667x + x2 = 1.333333333 The x term is -1.666666667x. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x + 0.6944444447 + x2 = 1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x + x2 = 1.333333333 + 0.6944444447 Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777 0.6944444447 + -1.666666667x + x2 = 2.0277777777 Factor a perfect square on the left side: (x + -0.8333333335)(x + -0.8333333335) = 2.0277777777 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x + -0.8333333335) equal to 1.424000624 and -1.424000624.Subproblem 1
x + -0.8333333335 = 1.424000624 Simplifying x + -0.8333333335 = 1.424000624 Reorder the terms: -0.8333333335 + x = 1.424000624 Solving -0.8333333335 + x = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = 1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = 1.424000624 + 0.8333333335 x = 1.424000624 + 0.8333333335 Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575 x = 2.2573339575 Simplifying x = 2.2573339575Subproblem 2
x + -0.8333333335 = -1.424000624 Simplifying x + -0.8333333335 = -1.424000624 Reorder the terms: -0.8333333335 + x = -1.424000624 Solving -0.8333333335 + x = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x = -1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x = -1.424000624 + 0.8333333335 x = -1.424000624 + 0.8333333335 Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905 x = -0.5906672905 Simplifying x = -0.5906672905Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.2573339575, -0.5906672905}Solution
x = {2.2573339575, -0.5906672905}
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