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Simplifying 6x2 + 48x + -45 = 0 Reorder the terms: -45 + 48x + 6x2 = 0 Solving -45 + 48x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-15 + 16x + 2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-15 + 16x + 2x2)' equal to zero and attempt to solve: Simplifying -15 + 16x + 2x2 = 0 Solving -15 + 16x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -7.5 + 8x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + 8x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + 8x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + 8x + x2 = 0 + 7.5 8x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 8x + x2 = 7.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 7.5 + 16 Reorder the terms: 16 + 8x + x2 = 7.5 + 16 Combine like terms: 7.5 + 16 = 23.5 16 + 8x + x2 = 23.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 23.5 Calculate the square root of the right side: 4.847679857 Break this problem into two subproblems by setting (x + 4) equal to 4.847679857 and -4.847679857.Subproblem 1
x + 4 = 4.847679857 Simplifying x + 4 = 4.847679857 Reorder the terms: 4 + x = 4.847679857 Solving 4 + x = 4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.847679857 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.847679857 + -4 x = 4.847679857 + -4 Combine like terms: 4.847679857 + -4 = 0.847679857 x = 0.847679857 Simplifying x = 0.847679857Subproblem 2
x + 4 = -4.847679857 Simplifying x + 4 = -4.847679857 Reorder the terms: 4 + x = -4.847679857 Solving 4 + x = -4.847679857 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.847679857 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.847679857 + -4 x = -4.847679857 + -4 Combine like terms: -4.847679857 + -4 = -8.847679857 x = -8.847679857 Simplifying x = -8.847679857Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.847679857, -8.847679857}Solution
x = {0.847679857, -8.847679857}
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