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Simplifying (20x)(20x) + 22x + -12 = 0 Remove parenthesis around (20x) 20x(20x) + 22x + -12 = 0 Remove parenthesis around (20x) 20x * 20x + 22x + -12 = 0 Reorder the terms for easier multiplication: 20 * 20x * x + 22x + -12 = 0 Multiply 20 * 20 400x * x + 22x + -12 = 0 Multiply x * x 400x2 + 22x + -12 = 0 Reorder the terms: -12 + 22x + 400x2 = 0 Solving -12 + 22x + 400x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 11x + 200x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 11x + 200x2)' equal to zero and attempt to solve: Simplifying -6 + 11x + 200x2 = 0 Solving -6 + 11x + 200x2 = 0 Begin completing the square. Divide all terms by 200 the coefficient of the squared term: Divide each side by '200'. -0.03 + 0.055x + x2 = 0.00 Move the constant term to the right: Add '0.03' to each side of the equation. -0.03 + 0.055x + 0.03 + x2 = 0.00 + 0.03 Reorder the terms: -0.03 + 0.03 + 0.055x + x2 = 0.00 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + 0.055x + x2 = 0.00 + 0.03 0.055x + x2 = 0.00 + 0.03 Combine like terms: 0.00 + 0.03 = 0.03 0.055x + x2 = 0.03 The x term is 0.055x. Take half its coefficient (0.0275). Square it (0.00075625) and add it to both sides. Add '0.00075625' to each side of the equation. 0.055x + 0.00075625 + x2 = 0.03 + 0.00075625 Reorder the terms: 0.00075625 + 0.055x + x2 = 0.03 + 0.00075625 Combine like terms: 0.03 + 0.00075625 = 0.03075625 0.00075625 + 0.055x + x2 = 0.03075625 Factor a perfect square on the left side: (x + 0.0275)(x + 0.0275) = 0.03075625 Calculate the square root of the right side: 0.175374599 Break this problem into two subproblems by setting (x + 0.0275) equal to 0.175374599 and -0.175374599.Subproblem 1
x + 0.0275 = 0.175374599 Simplifying x + 0.0275 = 0.175374599 Reorder the terms: 0.0275 + x = 0.175374599 Solving 0.0275 + x = 0.175374599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0275' to each side of the equation. 0.0275 + -0.0275 + x = 0.175374599 + -0.0275 Combine like terms: 0.0275 + -0.0275 = 0.0000 0.0000 + x = 0.175374599 + -0.0275 x = 0.175374599 + -0.0275 Combine like terms: 0.175374599 + -0.0275 = 0.147874599 x = 0.147874599 Simplifying x = 0.147874599Subproblem 2
x + 0.0275 = -0.175374599 Simplifying x + 0.0275 = -0.175374599 Reorder the terms: 0.0275 + x = -0.175374599 Solving 0.0275 + x = -0.175374599 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0275' to each side of the equation. 0.0275 + -0.0275 + x = -0.175374599 + -0.0275 Combine like terms: 0.0275 + -0.0275 = 0.0000 0.0000 + x = -0.175374599 + -0.0275 x = -0.175374599 + -0.0275 Combine like terms: -0.175374599 + -0.0275 = -0.202874599 x = -0.202874599 Simplifying x = -0.202874599Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.147874599, -0.202874599}Solution
x = {0.147874599, -0.202874599}
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