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Simplifying 300x2 + -120x + 8 = 0 Reorder the terms: 8 + -120x + 300x2 = 0 Solving 8 + -120x + 300x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + -30x + 75x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + -30x + 75x2)' equal to zero and attempt to solve: Simplifying 2 + -30x + 75x2 = 0 Solving 2 + -30x + 75x2 = 0 Begin completing the square. Divide all terms by 75 the coefficient of the squared term: Divide each side by '75'. 0.02666666667 + -0.4x + x2 = 0 Move the constant term to the right: Add '-0.02666666667' to each side of the equation. 0.02666666667 + -0.4x + -0.02666666667 + x2 = 0 + -0.02666666667 Reorder the terms: 0.02666666667 + -0.02666666667 + -0.4x + x2 = 0 + -0.02666666667 Combine like terms: 0.02666666667 + -0.02666666667 = 0.00000000000 0.00000000000 + -0.4x + x2 = 0 + -0.02666666667 -0.4x + x2 = 0 + -0.02666666667 Combine like terms: 0 + -0.02666666667 = -0.02666666667 -0.4x + x2 = -0.02666666667 The x term is -0.4x. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4x + 0.04 + x2 = -0.02666666667 + 0.04 Reorder the terms: 0.04 + -0.4x + x2 = -0.02666666667 + 0.04 Combine like terms: -0.02666666667 + 0.04 = 0.01333333333 0.04 + -0.4x + x2 = 0.01333333333 Factor a perfect square on the left side: (x + -0.2)(x + -0.2) = 0.01333333333 Calculate the square root of the right side: 0.115470054 Break this problem into two subproblems by setting (x + -0.2) equal to 0.115470054 and -0.115470054.Subproblem 1
x + -0.2 = 0.115470054 Simplifying x + -0.2 = 0.115470054 Reorder the terms: -0.2 + x = 0.115470054 Solving -0.2 + x = 0.115470054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 0.115470054 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 0.115470054 + 0.2 x = 0.115470054 + 0.2 Combine like terms: 0.115470054 + 0.2 = 0.315470054 x = 0.315470054 Simplifying x = 0.315470054Subproblem 2
x + -0.2 = -0.115470054 Simplifying x + -0.2 = -0.115470054 Reorder the terms: -0.2 + x = -0.115470054 Solving -0.2 + x = -0.115470054 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -0.115470054 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -0.115470054 + 0.2 x = -0.115470054 + 0.2 Combine like terms: -0.115470054 + 0.2 = 0.084529946 x = 0.084529946 Simplifying x = 0.084529946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.315470054, 0.084529946}Solution
x = {0.315470054, 0.084529946}
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