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Simplifying 5x(3x + 5) = 100 Reorder the terms: 5x(5 + 3x) = 100 (5 * 5x + 3x * 5x) = 100 (25x + 15x2) = 100 Solving 25x + 15x2 = 100 Solving for variable 'x'. Reorder the terms: -100 + 25x + 15x2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 25x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 5x + 3x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + 5x + 3x2)' equal to zero and attempt to solve: Simplifying -20 + 5x + 3x2 = 0 Solving -20 + 5x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + 1.666666667x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + 1.666666667x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + 1.666666667x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + 1.666666667x + x2 = 0 + 6.666666667 1.666666667x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 1.666666667x + x2 = 6.666666667 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 = 6.666666667 + 0.6944444447 Reorder the terms: 0.6944444447 + 1.666666667x + x2 = 6.666666667 + 0.6944444447 Combine like terms: 6.666666667 + 0.6944444447 = 7.3611111117 0.6944444447 + 1.666666667x + x2 = 7.3611111117 Factor a perfect square on the left side: (x + 0.8333333335)(x + 0.8333333335) = 7.3611111117 Calculate the square root of the right side: 2.713136766 Break this problem into two subproblems by setting (x + 0.8333333335) equal to 2.713136766 and -2.713136766.Subproblem 1
x + 0.8333333335 = 2.713136766 Simplifying x + 0.8333333335 = 2.713136766 Reorder the terms: 0.8333333335 + x = 2.713136766 Solving 0.8333333335 + x = 2.713136766 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 = 2.713136766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = 2.713136766 + -0.8333333335 x = 2.713136766 + -0.8333333335 Combine like terms: 2.713136766 + -0.8333333335 = 1.8798034325 x = 1.8798034325 Simplifying x = 1.8798034325Subproblem 2
x + 0.8333333335 = -2.713136766 Simplifying x + 0.8333333335 = -2.713136766 Reorder the terms: 0.8333333335 + x = -2.713136766 Solving 0.8333333335 + x = -2.713136766 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 = -2.713136766 + -0.8333333335 Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000 0.0000000000 + x = -2.713136766 + -0.8333333335 x = -2.713136766 + -0.8333333335 Combine like terms: -2.713136766 + -0.8333333335 = -3.5464700995 x = -3.5464700995 Simplifying x = -3.5464700995Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8798034325, -3.5464700995}Solution
x = {1.8798034325, -3.5464700995}
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