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Simplifying 32x2 + 104x + -72 = 0 Reorder the terms: -72 + 104x + 32x2 = 0 Solving -72 + 104x + 32x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '8'. 8(-9 + 13x + 4x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-9 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying -9 + 13x + 4x2 = 0 Solving -9 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + 3.25x + x2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + 3.25x + 2.25 + x2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + 3.25x + x2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + 3.25x + x2 = 0 + 2.25 3.25x + x2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 3.25x + x2 = 2.25 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 2.25 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 2.25 + 2.640625 Combine like terms: 2.25 + 2.640625 = 4.890625 2.640625 + 3.25x + x2 = 4.890625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 4.890625 Calculate the square root of the right side: 2.211475752 Break this problem into two subproblems by setting (x + 1.625) equal to 2.211475752 and -2.211475752.Subproblem 1
x + 1.625 = 2.211475752 Simplifying x + 1.625 = 2.211475752 Reorder the terms: 1.625 + x = 2.211475752 Solving 1.625 + x = 2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 2.211475752 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.211475752 + -1.625 x = 2.211475752 + -1.625 Combine like terms: 2.211475752 + -1.625 = 0.586475752 x = 0.586475752 Simplifying x = 0.586475752Subproblem 2
x + 1.625 = -2.211475752 Simplifying x + 1.625 = -2.211475752 Reorder the terms: 1.625 + x = -2.211475752 Solving 1.625 + x = -2.211475752 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -2.211475752 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.211475752 + -1.625 x = -2.211475752 + -1.625 Combine like terms: -2.211475752 + -1.625 = -3.836475752 x = -3.836475752 Simplifying x = -3.836475752Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.586475752, -3.836475752}Solution
x = {0.586475752, -3.836475752}
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