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Simplifying 5x + 5 = 3(5x + 4) * 10x Reorder the terms: 5 + 5x = 3(5x + 4) * 10x Reorder the terms: 5 + 5x = 3(4 + 5x) * 10x Reorder the terms for easier multiplication: 5 + 5x = 3 * 10x(4 + 5x) Multiply 3 * 10 5 + 5x = 30x(4 + 5x) 5 + 5x = (4 * 30x + 5x * 30x) 5 + 5x = (120x + 150x2) Solving 5 + 5x = 120x + 150x2 Solving for variable 'x'. Combine like terms: 5x + -120x = -115x 5 + -115x + -150x2 = 120x + 150x2 + -120x + -150x2 Reorder the terms: 5 + -115x + -150x2 = 120x + -120x + 150x2 + -150x2 Combine like terms: 120x + -120x = 0 5 + -115x + -150x2 = 0 + 150x2 + -150x2 5 + -115x + -150x2 = 150x2 + -150x2 Combine like terms: 150x2 + -150x2 = 0 5 + -115x + -150x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -23x + -30x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -23x + -30x2)' equal to zero and attempt to solve: Simplifying 1 + -23x + -30x2 = 0 Solving 1 + -23x + -30x2 = 0 Begin completing the square. Divide all terms by -30 the coefficient of the squared term: Divide each side by '-30'. -0.03333333333 + 0.7666666667x + x2 = 0.0 Move the constant term to the right: Add '0.03333333333' to each side of the equation. -0.03333333333 + 0.7666666667x + 0.03333333333 + x2 = 0.0 + 0.03333333333 Reorder the terms: -0.03333333333 + 0.03333333333 + 0.7666666667x + x2 = 0.0 + 0.03333333333 Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000 0.00000000000 + 0.7666666667x + x2 = 0.0 + 0.03333333333 0.7666666667x + x2 = 0.0 + 0.03333333333 Combine like terms: 0.0 + 0.03333333333 = 0.03333333333 0.7666666667x + x2 = 0.03333333333 The x term is 0.7666666667x. Take half its coefficient (0.3833333334). Square it (0.1469444445) and add it to both sides. Add '0.1469444445' to each side of the equation. 0.7666666667x + 0.1469444445 + x2 = 0.03333333333 + 0.1469444445 Reorder the terms: 0.1469444445 + 0.7666666667x + x2 = 0.03333333333 + 0.1469444445 Combine like terms: 0.03333333333 + 0.1469444445 = 0.18027777783 0.1469444445 + 0.7666666667x + x2 = 0.18027777783 Factor a perfect square on the left side: (x + 0.3833333334)(x + 0.3833333334) = 0.18027777783 Calculate the square root of the right side: 0.424591307 Break this problem into two subproblems by setting (x + 0.3833333334) equal to 0.424591307 and -0.424591307.Subproblem 1
x + 0.3833333334 = 0.424591307 Simplifying x + 0.3833333334 = 0.424591307 Reorder the terms: 0.3833333334 + x = 0.424591307 Solving 0.3833333334 + x = 0.424591307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3833333334' to each side of the equation. 0.3833333334 + -0.3833333334 + x = 0.424591307 + -0.3833333334 Combine like terms: 0.3833333334 + -0.3833333334 = 0.0000000000 0.0000000000 + x = 0.424591307 + -0.3833333334 x = 0.424591307 + -0.3833333334 Combine like terms: 0.424591307 + -0.3833333334 = 0.0412579736 x = 0.0412579736 Simplifying x = 0.0412579736Subproblem 2
x + 0.3833333334 = -0.424591307 Simplifying x + 0.3833333334 = -0.424591307 Reorder the terms: 0.3833333334 + x = -0.424591307 Solving 0.3833333334 + x = -0.424591307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3833333334' to each side of the equation. 0.3833333334 + -0.3833333334 + x = -0.424591307 + -0.3833333334 Combine like terms: 0.3833333334 + -0.3833333334 = 0.0000000000 0.0000000000 + x = -0.424591307 + -0.3833333334 x = -0.424591307 + -0.3833333334 Combine like terms: -0.424591307 + -0.3833333334 = -0.8079246404 x = -0.8079246404 Simplifying x = -0.8079246404Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.0412579736, -0.8079246404}Solution
x = {0.0412579736, -0.8079246404}
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