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Simplifying 0 = 24x2 + -1800x + 20 Reorder the terms: 0 = 20 + -1800x + 24x2 Solving 0 = 20 + -1800x + 24x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 1800x + -24x2 = 20 + -1800x + 24x2 + -20 + 1800x + -24x2 Reorder the terms: -20 + 1800x + -24x2 = 20 + -20 + -1800x + 1800x + 24x2 + -24x2 Combine like terms: 20 + -20 = 0 -20 + 1800x + -24x2 = 0 + -1800x + 1800x + 24x2 + -24x2 -20 + 1800x + -24x2 = -1800x + 1800x + 24x2 + -24x2 Combine like terms: -1800x + 1800x = 0 -20 + 1800x + -24x2 = 0 + 24x2 + -24x2 -20 + 1800x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 -20 + 1800x + -24x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 450x + -6x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 450x + -6x2)' equal to zero and attempt to solve: Simplifying -5 + 450x + -6x2 = 0 Solving -5 + 450x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.8333333333 + -75x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -75x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -75x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -75x + x2 = 0 + -0.8333333333 -75x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -75x + x2 = -0.8333333333 The x term is -75x. Take half its coefficient (-37.5). Square it (1406.25) and add it to both sides. Add '1406.25' to each side of the equation. -75x + 1406.25 + x2 = -0.8333333333 + 1406.25 Reorder the terms: 1406.25 + -75x + x2 = -0.8333333333 + 1406.25 Combine like terms: -0.8333333333 + 1406.25 = 1405.4166666667 1406.25 + -75x + x2 = 1405.4166666667 Factor a perfect square on the left side: (x + -37.5)(x + -37.5) = 1405.4166666667 Calculate the square root of the right side: 37.488887242 Break this problem into two subproblems by setting (x + -37.5) equal to 37.488887242 and -37.488887242.Subproblem 1
x + -37.5 = 37.488887242 Simplifying x + -37.5 = 37.488887242 Reorder the terms: -37.5 + x = 37.488887242 Solving -37.5 + x = 37.488887242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = 37.488887242 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = 37.488887242 + 37.5 x = 37.488887242 + 37.5 Combine like terms: 37.488887242 + 37.5 = 74.988887242 x = 74.988887242 Simplifying x = 74.988887242Subproblem 2
x + -37.5 = -37.488887242 Simplifying x + -37.5 = -37.488887242 Reorder the terms: -37.5 + x = -37.488887242 Solving -37.5 + x = -37.488887242 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37.5' to each side of the equation. -37.5 + 37.5 + x = -37.488887242 + 37.5 Combine like terms: -37.5 + 37.5 = 0.0 0.0 + x = -37.488887242 + 37.5 x = -37.488887242 + 37.5 Combine like terms: -37.488887242 + 37.5 = 0.011112758 x = 0.011112758 Simplifying x = 0.011112758Solution
The solution to the problem is based on the solutions from the subproblems. x = {74.988887242, 0.011112758}Solution
x = {74.988887242, 0.011112758}
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