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Simplifying 48 + 16x + -10x2 = 0 Solving 48 + 16x + -10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(24 + 8x + -5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(24 + 8x + -5x2)' equal to zero and attempt to solve: Simplifying 24 + 8x + -5x2 = 0 Solving 24 + 8x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.8 + -1.6x + x2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -1.6x + 4.8 + x2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -1.6x + x2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -1.6x + x2 = 0 + 4.8 -1.6x + x2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -1.6x + x2 = 4.8 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = 4.8 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = 4.8 + 0.64 Combine like terms: 4.8 + 0.64 = 5.44 0.64 + -1.6x + x2 = 5.44 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (x + -0.8) equal to 2.332380758 and -2.332380758.Subproblem 1
x + -0.8 = 2.332380758 Simplifying x + -0.8 = 2.332380758 Reorder the terms: -0.8 + x = 2.332380758 Solving -0.8 + x = 2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = 2.332380758 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = 2.332380758 + 0.8 x = 2.332380758 + 0.8 Combine like terms: 2.332380758 + 0.8 = 3.132380758 x = 3.132380758 Simplifying x = 3.132380758Subproblem 2
x + -0.8 = -2.332380758 Simplifying x + -0.8 = -2.332380758 Reorder the terms: -0.8 + x = -2.332380758 Solving -0.8 + x = -2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8' to each side of the equation. -0.8 + 0.8 + x = -2.332380758 + 0.8 Combine like terms: -0.8 + 0.8 = 0.0 0.0 + x = -2.332380758 + 0.8 x = -2.332380758 + 0.8 Combine like terms: -2.332380758 + 0.8 = -1.532380758 x = -1.532380758 Simplifying x = -1.532380758Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.132380758, -1.532380758}Solution
x = {3.132380758, -1.532380758}
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