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Simplifying 56 = 0.5 * 32x2 + 60x + 6 Multiply 0.5 * 32 56 = 16x2 + 60x + 6 Reorder the terms: 56 = 6 + 60x + 16x2 Solving 56 = 6 + 60x + 16x2 Solving for variable 'x'. Combine like terms: 56 + -6 = 50 50 + -60x + -16x2 = 6 + 60x + 16x2 + -6 + -60x + -16x2 Reorder the terms: 50 + -60x + -16x2 = 6 + -6 + 60x + -60x + 16x2 + -16x2 Combine like terms: 6 + -6 = 0 50 + -60x + -16x2 = 0 + 60x + -60x + 16x2 + -16x2 50 + -60x + -16x2 = 60x + -60x + 16x2 + -16x2 Combine like terms: 60x + -60x = 0 50 + -60x + -16x2 = 0 + 16x2 + -16x2 50 + -60x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 50 + -60x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(25 + -30x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(25 + -30x + -8x2)' equal to zero and attempt to solve: Simplifying 25 + -30x + -8x2 = 0 Solving 25 + -30x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -3.125 + 3.75x + x2 = 0 Move the constant term to the right: Add '3.125' to each side of the equation. -3.125 + 3.75x + 3.125 + x2 = 0 + 3.125 Reorder the terms: -3.125 + 3.125 + 3.75x + x2 = 0 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + 3.75x + x2 = 0 + 3.125 3.75x + x2 = 0 + 3.125 Combine like terms: 0 + 3.125 = 3.125 3.75x + x2 = 3.125 The x term is 3.75x. Take half its coefficient (1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. 3.75x + 3.515625 + x2 = 3.125 + 3.515625 Reorder the terms: 3.515625 + 3.75x + x2 = 3.125 + 3.515625 Combine like terms: 3.125 + 3.515625 = 6.640625 3.515625 + 3.75x + x2 = 6.640625 Factor a perfect square on the left side: (x + 1.875)(x + 1.875) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (x + 1.875) equal to 2.576941016 and -2.576941016.Subproblem 1
x + 1.875 = 2.576941016 Simplifying x + 1.875 = 2.576941016 Reorder the terms: 1.875 + x = 2.576941016 Solving 1.875 + x = 2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = 2.576941016 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = 2.576941016 + -1.875 x = 2.576941016 + -1.875 Combine like terms: 2.576941016 + -1.875 = 0.701941016 x = 0.701941016 Simplifying x = 0.701941016Subproblem 2
x + 1.875 = -2.576941016 Simplifying x + 1.875 = -2.576941016 Reorder the terms: 1.875 + x = -2.576941016 Solving 1.875 + x = -2.576941016 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.875' to each side of the equation. 1.875 + -1.875 + x = -2.576941016 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + x = -2.576941016 + -1.875 x = -2.576941016 + -1.875 Combine like terms: -2.576941016 + -1.875 = -4.451941016 x = -4.451941016 Simplifying x = -4.451941016Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.701941016, -4.451941016}Solution
x = {0.701941016, -4.451941016}
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