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Simplifying -0.5(32x2) + 60x + 60 = 56 Remove parenthesis around (32x2) -0.5 * 32x2 + 60x + 60 = 56 Multiply -0.5 * 32 -16x2 + 60x + 60 = 56 Reorder the terms: 60 + 60x + -16x2 = 56 Solving 60 + 60x + -16x2 = 56 Solving for variable 'x'. Reorder the terms: 60 + -56 + 60x + -16x2 = 56 + -56 Combine like terms: 60 + -56 = 4 4 + 60x + -16x2 = 56 + -56 Combine like terms: 56 + -56 = 0 4 + 60x + -16x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 15x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 15x + -4x2)' equal to zero and attempt to solve: Simplifying 1 + 15x + -4x2 = 0 Solving 1 + 15x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.25 + -3.75x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -3.75x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -3.75x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -3.75x + x2 = 0 + 0.25 -3.75x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -3.75x + x2 = 0.25 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 = 0.25 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 0.25 + 3.515625 Combine like terms: 0.25 + 3.515625 = 3.765625 3.515625 + -3.75x + x2 = 3.765625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 3.765625 Calculate the square root of the right side: 1.940521837 Break this problem into two subproblems by setting (x + -1.875) equal to 1.940521837 and -1.940521837.Subproblem 1
x + -1.875 = 1.940521837 Simplifying x + -1.875 = 1.940521837 Reorder the terms: -1.875 + x = 1.940521837 Solving -1.875 + x = 1.940521837 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 = 1.940521837 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 1.940521837 + 1.875 x = 1.940521837 + 1.875 Combine like terms: 1.940521837 + 1.875 = 3.815521837 x = 3.815521837 Simplifying x = 3.815521837Subproblem 2
x + -1.875 = -1.940521837 Simplifying x + -1.875 = -1.940521837 Reorder the terms: -1.875 + x = -1.940521837 Solving -1.875 + x = -1.940521837 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 = -1.940521837 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -1.940521837 + 1.875 x = -1.940521837 + 1.875 Combine like terms: -1.940521837 + 1.875 = -0.065521837 x = -0.065521837 Simplifying x = -0.065521837Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.815521837, -0.065521837}Solution
x = {3.815521837, -0.065521837}
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