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Simplifying -64x2 + -12x + 210 = 0 Reorder the terms: 210 + -12x + -64x2 = 0 Solving 210 + -12x + -64x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(105 + -6x + -32x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(105 + -6x + -32x2)' equal to zero and attempt to solve: Simplifying 105 + -6x + -32x2 = 0 Solving 105 + -6x + -32x2 = 0 Begin completing the square. Divide all terms by -32 the coefficient of the squared term: Divide each side by '-32'. -3.28125 + 0.1875x + x2 = 0 Move the constant term to the right: Add '3.28125' to each side of the equation. -3.28125 + 0.1875x + 3.28125 + x2 = 0 + 3.28125 Reorder the terms: -3.28125 + 3.28125 + 0.1875x + x2 = 0 + 3.28125 Combine like terms: -3.28125 + 3.28125 = 0.00000 0.00000 + 0.1875x + x2 = 0 + 3.28125 0.1875x + x2 = 0 + 3.28125 Combine like terms: 0 + 3.28125 = 3.28125 0.1875x + x2 = 3.28125 The x term is 0.1875x. Take half its coefficient (0.09375). Square it (0.0087890625) and add it to both sides. Add '0.0087890625' to each side of the equation. 0.1875x + 0.0087890625 + x2 = 3.28125 + 0.0087890625 Reorder the terms: 0.0087890625 + 0.1875x + x2 = 3.28125 + 0.0087890625 Combine like terms: 3.28125 + 0.0087890625 = 3.2900390625 0.0087890625 + 0.1875x + x2 = 3.2900390625 Factor a perfect square on the left side: (x + 0.09375)(x + 0.09375) = 3.2900390625 Calculate the square root of the right side: 1.813846483 Break this problem into two subproblems by setting (x + 0.09375) equal to 1.813846483 and -1.813846483.Subproblem 1
x + 0.09375 = 1.813846483 Simplifying x + 0.09375 = 1.813846483 Reorder the terms: 0.09375 + x = 1.813846483 Solving 0.09375 + x = 1.813846483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = 1.813846483 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = 1.813846483 + -0.09375 x = 1.813846483 + -0.09375 Combine like terms: 1.813846483 + -0.09375 = 1.720096483 x = 1.720096483 Simplifying x = 1.720096483Subproblem 2
x + 0.09375 = -1.813846483 Simplifying x + 0.09375 = -1.813846483 Reorder the terms: 0.09375 + x = -1.813846483 Solving 0.09375 + x = -1.813846483 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.09375' to each side of the equation. 0.09375 + -0.09375 + x = -1.813846483 + -0.09375 Combine like terms: 0.09375 + -0.09375 = 0.00000 0.00000 + x = -1.813846483 + -0.09375 x = -1.813846483 + -0.09375 Combine like terms: -1.813846483 + -0.09375 = -1.907596483 x = -1.907596483 Simplifying x = -1.907596483Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.720096483, -1.907596483}Solution
x = {1.720096483, -1.907596483}
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