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Simplifying -8x2 = 48x + -40 Reorder the terms: -8x2 = -40 + 48x Solving -8x2 = -40 + 48x Solving for variable 'x'. Reorder the terms: 40 + -48x + -8x2 = -40 + 48x + 40 + -48x Reorder the terms: 40 + -48x + -8x2 = -40 + 40 + 48x + -48x Combine like terms: -40 + 40 = 0 40 + -48x + -8x2 = 0 + 48x + -48x 40 + -48x + -8x2 = 48x + -48x Combine like terms: 48x + -48x = 0 40 + -48x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(5 + -6x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(5 + -6x + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -6x + -1x2 = 0 Solving 5 + -6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + 6x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + 6x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 6x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 6x + x2 = 0 + 5 6x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 6x + x2 = 5 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 5 + 9 Reorder the terms: 9 + 6x + x2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + 6x + x2 = 14 Factor a perfect square on the left side: (x + 3)(x + 3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (x + 3) equal to 3.741657387 and -3.741657387.Subproblem 1
x + 3 = 3.741657387 Simplifying x + 3 = 3.741657387 Reorder the terms: 3 + x = 3.741657387 Solving 3 + x = 3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.741657387 + -3 x = 3.741657387 + -3 Combine like terms: 3.741657387 + -3 = 0.741657387 x = 0.741657387 Simplifying x = 0.741657387Subproblem 2
x + 3 = -3.741657387 Simplifying x + 3 = -3.741657387 Reorder the terms: 3 + x = -3.741657387 Solving 3 + x = -3.741657387 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -3.741657387 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.741657387 + -3 x = -3.741657387 + -3 Combine like terms: -3.741657387 + -3 = -6.741657387 x = -6.741657387 Simplifying x = -6.741657387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.741657387, -6.741657387}Solution
x = {0.741657387, -6.741657387}
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