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Simplifying -5X2 + -28X = 12 Reorder the terms: -28X + -5X2 = 12 Solving -28X + -5X2 = 12 Solving for variable 'X'. Reorder the terms: -12 + -28X + -5X2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -28X + -5X2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + 28X + 5X2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + 28X + 5X2)' equal to zero and attempt to solve: Simplifying 12 + 28X + 5X2 = 0 Solving 12 + 28X + 5X2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + 5.6X + X2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + 5.6X + -2.4 + X2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + 5.6X + X2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + 5.6X + X2 = 0 + -2.4 5.6X + X2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 5.6X + X2 = -2.4 The X term is 5.6X. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6X + 7.84 + X2 = -2.4 + 7.84 Reorder the terms: 7.84 + 5.6X + X2 = -2.4 + 7.84 Combine like terms: -2.4 + 7.84 = 5.44 7.84 + 5.6X + X2 = 5.44 Factor a perfect square on the left side: (X + 2.8)(X + 2.8) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (X + 2.8) equal to 2.332380758 and -2.332380758.Subproblem 1
X + 2.8 = 2.332380758 Simplifying X + 2.8 = 2.332380758 Reorder the terms: 2.8 + X = 2.332380758 Solving 2.8 + X = 2.332380758 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + X = 2.332380758 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + X = 2.332380758 + -2.8 X = 2.332380758 + -2.8 Combine like terms: 2.332380758 + -2.8 = -0.467619242 X = -0.467619242 Simplifying X = -0.467619242Subproblem 2
X + 2.8 = -2.332380758 Simplifying X + 2.8 = -2.332380758 Reorder the terms: 2.8 + X = -2.332380758 Solving 2.8 + X = -2.332380758 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + X = -2.332380758 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + X = -2.332380758 + -2.8 X = -2.332380758 + -2.8 Combine like terms: -2.332380758 + -2.8 = -5.132380758 X = -5.132380758 Simplifying X = -5.132380758Solution
The solution to the problem is based on the solutions from the subproblems. X = {-0.467619242, -5.132380758}Solution
X = {-0.467619242, -5.132380758}
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