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Simplifying 40x + 4x2 + -304 = 0 Reorder the terms: -304 + 40x + 4x2 = 0 Solving -304 + 40x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-76 + 10x + x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-76 + 10x + x2)' equal to zero and attempt to solve: Simplifying -76 + 10x + x2 = 0 Solving -76 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '76' to each side of the equation. -76 + 10x + 76 + x2 = 0 + 76 Reorder the terms: -76 + 76 + 10x + x2 = 0 + 76 Combine like terms: -76 + 76 = 0 0 + 10x + x2 = 0 + 76 10x + x2 = 0 + 76 Combine like terms: 0 + 76 = 76 10x + x2 = 76 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 76 + 25 Reorder the terms: 25 + 10x + x2 = 76 + 25 Combine like terms: 76 + 25 = 101 25 + 10x + x2 = 101 Factor a perfect square on the left side: (x + 5)(x + 5) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (x + 5) equal to 10.049875621 and -10.049875621.Subproblem 1
x + 5 = 10.049875621 Simplifying x + 5 = 10.049875621 Reorder the terms: 5 + x = 10.049875621 Solving 5 + x = 10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 10.049875621 + -5 Combine like terms: 5 + -5 = 0 0 + x = 10.049875621 + -5 x = 10.049875621 + -5 Combine like terms: 10.049875621 + -5 = 5.049875621 x = 5.049875621 Simplifying x = 5.049875621Subproblem 2
x + 5 = -10.049875621 Simplifying x + 5 = -10.049875621 Reorder the terms: 5 + x = -10.049875621 Solving 5 + x = -10.049875621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -10.049875621 + -5 Combine like terms: 5 + -5 = 0 0 + x = -10.049875621 + -5 x = -10.049875621 + -5 Combine like terms: -10.049875621 + -5 = -15.049875621 x = -15.049875621 Simplifying x = -15.049875621Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.049875621, -15.049875621}Solution
x = {5.049875621, -15.049875621}
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