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Simplifying 4x2 + 30x = 20 Reorder the terms: 30x + 4x2 = 20 Solving 30x + 4x2 = 20 Solving for variable 'x'. Reorder the terms: -20 + 30x + 4x2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 30x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 15x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 15x + 2x2)' equal to zero and attempt to solve: Simplifying -10 + 15x + 2x2 = 0 Solving -10 + 15x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -5 + 7.5x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 7.5x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 7.5x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 7.5x + x2 = 0 + 5 7.5x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 7.5x + x2 = 5 The x term is 7.5x. Take half its coefficient (3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. 7.5x + 14.0625 + x2 = 5 + 14.0625 Reorder the terms: 14.0625 + 7.5x + x2 = 5 + 14.0625 Combine like terms: 5 + 14.0625 = 19.0625 14.0625 + 7.5x + x2 = 19.0625 Factor a perfect square on the left side: (x + 3.75)(x + 3.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (x + 3.75) equal to 4.366062299 and -4.366062299.Subproblem 1
x + 3.75 = 4.366062299 Simplifying x + 3.75 = 4.366062299 Reorder the terms: 3.75 + x = 4.366062299 Solving 3.75 + x = 4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = 4.366062299 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = 4.366062299 + -3.75 x = 4.366062299 + -3.75 Combine like terms: 4.366062299 + -3.75 = 0.616062299 x = 0.616062299 Simplifying x = 0.616062299Subproblem 2
x + 3.75 = -4.366062299 Simplifying x + 3.75 = -4.366062299 Reorder the terms: 3.75 + x = -4.366062299 Solving 3.75 + x = -4.366062299 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.75' to each side of the equation. 3.75 + -3.75 + x = -4.366062299 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + x = -4.366062299 + -3.75 x = -4.366062299 + -3.75 Combine like terms: -4.366062299 + -3.75 = -8.116062299 x = -8.116062299 Simplifying x = -8.116062299Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.616062299, -8.116062299}Solution
x = {0.616062299, -8.116062299}
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