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Simplifying -5x2 + -38x + -45 = 0 Reorder the terms: -45 + -38x + -5x2 = 0 Solving -45 + -38x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(45 + 38x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 38x + 5x2)' equal to zero and attempt to solve: Simplifying 45 + 38x + 5x2 = 0 Solving 45 + 38x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 9 + 7.6x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + 7.6x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 7.6x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 7.6x + x2 = 0 + -9 7.6x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 7.6x + x2 = -9 The x term is 7.6x. Take half its coefficient (3.8). Square it (14.44) and add it to both sides. Add '14.44' to each side of the equation. 7.6x + 14.44 + x2 = -9 + 14.44 Reorder the terms: 14.44 + 7.6x + x2 = -9 + 14.44 Combine like terms: -9 + 14.44 = 5.44 14.44 + 7.6x + x2 = 5.44 Factor a perfect square on the left side: (x + 3.8)(x + 3.8) = 5.44 Calculate the square root of the right side: 2.332380758 Break this problem into two subproblems by setting (x + 3.8) equal to 2.332380758 and -2.332380758.Subproblem 1
x + 3.8 = 2.332380758 Simplifying x + 3.8 = 2.332380758 Reorder the terms: 3.8 + x = 2.332380758 Solving 3.8 + x = 2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = 2.332380758 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = 2.332380758 + -3.8 x = 2.332380758 + -3.8 Combine like terms: 2.332380758 + -3.8 = -1.467619242 x = -1.467619242 Simplifying x = -1.467619242Subproblem 2
x + 3.8 = -2.332380758 Simplifying x + 3.8 = -2.332380758 Reorder the terms: 3.8 + x = -2.332380758 Solving 3.8 + x = -2.332380758 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.8' to each side of the equation. 3.8 + -3.8 + x = -2.332380758 + -3.8 Combine like terms: 3.8 + -3.8 = 0.0 0.0 + x = -2.332380758 + -3.8 x = -2.332380758 + -3.8 Combine like terms: -2.332380758 + -3.8 = -6.132380758 x = -6.132380758 Simplifying x = -6.132380758Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.467619242, -6.132380758}Solution
x = {-1.467619242, -6.132380758}
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