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Simplifying 8x2 = 56x + -12 Reorder the terms: 8x2 = -12 + 56x Solving 8x2 = -12 + 56x Solving for variable 'x'. Reorder the terms: 12 + -56x + 8x2 = -12 + 56x + 12 + -56x Reorder the terms: 12 + -56x + 8x2 = -12 + 12 + 56x + -56x Combine like terms: -12 + 12 = 0 12 + -56x + 8x2 = 0 + 56x + -56x 12 + -56x + 8x2 = 56x + -56x Combine like terms: 56x + -56x = 0 12 + -56x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -14x + 2x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3 + -14x + 2x2)' equal to zero and attempt to solve: Simplifying 3 + -14x + 2x2 = 0 Solving 3 + -14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1.5 + -7x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -7x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -7x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -7x + x2 = 0 + -1.5 -7x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -7x + x2 = -1.5 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -1.5 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -1.5 + 12.25 Combine like terms: -1.5 + 12.25 = 10.75 12.25 + -7x + x2 = 10.75 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + -3.5) equal to 3.278719262 and -3.278719262.Subproblem 1
x + -3.5 = 3.278719262 Simplifying x + -3.5 = 3.278719262 Reorder the terms: -3.5 + x = 3.278719262 Solving -3.5 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 3.278719262 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 3.278719262 + 3.5 x = 3.278719262 + 3.5 Combine like terms: 3.278719262 + 3.5 = 6.778719262 x = 6.778719262 Simplifying x = 6.778719262Subproblem 2
x + -3.5 = -3.278719262 Simplifying x + -3.5 = -3.278719262 Reorder the terms: -3.5 + x = -3.278719262 Solving -3.5 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -3.278719262 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -3.278719262 + 3.5 x = -3.278719262 + 3.5 Combine like terms: -3.278719262 + 3.5 = 0.221280738 x = 0.221280738 Simplifying x = 0.221280738Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.778719262, 0.221280738}Solution
x = {6.778719262, 0.221280738}
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