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Simplifying -16x2 + 126x + -192 = 0 Reorder the terms: -192 + 126x + -16x2 = 0 Solving -192 + 126x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-96 + 63x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-96 + 63x + -8x2)' equal to zero and attempt to solve: Simplifying -96 + 63x + -8x2 = 0 Solving -96 + 63x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 12 + -7.875x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.875x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7.875x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.875x + x2 = 0 + -12 -7.875x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.875x + x2 = -12 The x term is -7.875x. Take half its coefficient (-3.9375). Square it (15.50390625) and add it to both sides. Add '15.50390625' to each side of the equation. -7.875x + 15.50390625 + x2 = -12 + 15.50390625 Reorder the terms: 15.50390625 + -7.875x + x2 = -12 + 15.50390625 Combine like terms: -12 + 15.50390625 = 3.50390625 15.50390625 + -7.875x + x2 = 3.50390625 Factor a perfect square on the left side: (x + -3.9375)(x + -3.9375) = 3.50390625 Calculate the square root of the right side: 1.871872391 Break this problem into two subproblems by setting (x + -3.9375) equal to 1.871872391 and -1.871872391.Subproblem 1
x + -3.9375 = 1.871872391 Simplifying x + -3.9375 = 1.871872391 Reorder the terms: -3.9375 + x = 1.871872391 Solving -3.9375 + x = 1.871872391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + x = 1.871872391 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + x = 1.871872391 + 3.9375 x = 1.871872391 + 3.9375 Combine like terms: 1.871872391 + 3.9375 = 5.809372391 x = 5.809372391 Simplifying x = 5.809372391Subproblem 2
x + -3.9375 = -1.871872391 Simplifying x + -3.9375 = -1.871872391 Reorder the terms: -3.9375 + x = -1.871872391 Solving -3.9375 + x = -1.871872391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9375' to each side of the equation. -3.9375 + 3.9375 + x = -1.871872391 + 3.9375 Combine like terms: -3.9375 + 3.9375 = 0.0000 0.0000 + x = -1.871872391 + 3.9375 x = -1.871872391 + 3.9375 Combine like terms: -1.871872391 + 3.9375 = 2.065627609 x = 2.065627609 Simplifying x = 2.065627609Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.809372391, 2.065627609}Solution
x = {5.809372391, 2.065627609}
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