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Simplifying 60 = 24x + -2x2 Solving 60 = 24x + -2x2 Solving for variable 'x'. Reorder the terms: 60 + -24x + 2x2 = 24x + -24x + -2x2 + 2x2 Combine like terms: 24x + -24x = 0 60 + -24x + 2x2 = 0 + -2x2 + 2x2 60 + -24x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 60 + -24x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(30 + -12x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + -12x + x2)' equal to zero and attempt to solve: Simplifying 30 + -12x + x2 = 0 Solving 30 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -12x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12x + x2 = 0 + -30 -12x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12x + x2 = -30 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = -30 + 36 Reorder the terms: 36 + -12x + x2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12x + x2 = 6 Factor a perfect square on the left side: (x + -6)(x + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -6 = 2.449489743 Simplifying x + -6 = 2.449489743 Reorder the terms: -6 + x = 2.449489743 Solving -6 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + x = 2.449489743 + 6 x = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 x = 8.449489743 Simplifying x = 8.449489743Subproblem 2
x + -6 = -2.449489743 Simplifying x + -6 = -2.449489743 Reorder the terms: -6 + x = -2.449489743 Solving -6 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + x = -2.449489743 + 6 x = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 x = 3.550510257 Simplifying x = 3.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.449489743, 3.550510257}Solution
x = {8.449489743, 3.550510257}
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