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Simplifying 8x2 + -32x = 54 Reorder the terms: -32x + 8x2 = 54 Solving -32x + 8x2 = 54 Solving for variable 'x'. Reorder the terms: -54 + -32x + 8x2 = 54 + -54 Combine like terms: 54 + -54 = 0 -54 + -32x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -16x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-27 + -16x + 4x2)' equal to zero and attempt to solve: Simplifying -27 + -16x + 4x2 = 0 Solving -27 + -16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -4x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -4x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -4x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -4x + x2 = 0 + 6.75 -4x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -4x + x2 = 6.75 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 6.75 + 4 Reorder the terms: 4 + -4x + x2 = 6.75 + 4 Combine like terms: 6.75 + 4 = 10.75 4 + -4x + x2 = 10.75 Factor a perfect square on the left side: (x + -2)(x + -2) = 10.75 Calculate the square root of the right side: 3.278719262 Break this problem into two subproblems by setting (x + -2) equal to 3.278719262 and -3.278719262.Subproblem 1
x + -2 = 3.278719262 Simplifying x + -2 = 3.278719262 Reorder the terms: -2 + x = 3.278719262 Solving -2 + x = 3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 3.278719262 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.278719262 + 2 x = 3.278719262 + 2 Combine like terms: 3.278719262 + 2 = 5.278719262 x = 5.278719262 Simplifying x = 5.278719262Subproblem 2
x + -2 = -3.278719262 Simplifying x + -2 = -3.278719262 Reorder the terms: -2 + x = -3.278719262 Solving -2 + x = -3.278719262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -3.278719262 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.278719262 + 2 x = -3.278719262 + 2 Combine like terms: -3.278719262 + 2 = -1.278719262 x = -1.278719262 Simplifying x = -1.278719262Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.278719262, -1.278719262}Solution
x = {5.278719262, -1.278719262}
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