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Simplifying 20x2 + 28x = 120 Reorder the terms: 28x + 20x2 = 120 Solving 28x + 20x2 = 120 Solving for variable 'x'. Reorder the terms: -120 + 28x + 20x2 = 120 + -120 Combine like terms: 120 + -120 = 0 -120 + 28x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-30 + 7x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-30 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying -30 + 7x + 5x2 = 0 Solving -30 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -6 + 1.4x + x2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + 1.4x + 6 + x2 = 0 + 6 Reorder the terms: -6 + 6 + 1.4x + x2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + 1.4x + x2 = 0 + 6 1.4x + x2 = 0 + 6 Combine like terms: 0 + 6 = 6 1.4x + x2 = 6 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 6 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 6 + 0.49 Combine like terms: 6 + 0.49 = 6.49 0.49 + 1.4x + x2 = 6.49 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 6.49 Calculate the square root of the right side: 2.547547841 Break this problem into two subproblems by setting (x + 0.7) equal to 2.547547841 and -2.547547841.Subproblem 1
x + 0.7 = 2.547547841 Simplifying x + 0.7 = 2.547547841 Reorder the terms: 0.7 + x = 2.547547841 Solving 0.7 + x = 2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 2.547547841 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.547547841 + -0.7 x = 2.547547841 + -0.7 Combine like terms: 2.547547841 + -0.7 = 1.847547841 x = 1.847547841 Simplifying x = 1.847547841Subproblem 2
x + 0.7 = -2.547547841 Simplifying x + 0.7 = -2.547547841 Reorder the terms: 0.7 + x = -2.547547841 Solving 0.7 + x = -2.547547841 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -2.547547841 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.547547841 + -0.7 x = -2.547547841 + -0.7 Combine like terms: -2.547547841 + -0.7 = -3.247547841 x = -3.247547841 Simplifying x = -3.247547841Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.847547841, -3.247547841}Solution
x = {1.847547841, -3.247547841}
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