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Simplifying 16x2 + -16x + -42 = 0 Reorder the terms: -42 + -16x + 16x2 = 0 Solving -42 + -16x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + -8x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + -8x + 8x2)' equal to zero and attempt to solve: Simplifying -21 + -8x + 8x2 = 0 Solving -21 + -8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.625 + -1x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -1x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -1x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -1x + x2 = 0 + 2.625 -1x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -1x + x2 = 2.625 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 2.625 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 2.625 + 0.25 Combine like terms: 2.625 + 0.25 = 2.875 0.25 + -1x + x2 = 2.875 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -0.5) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -0.5 = 1.695582496 Simplifying x + -0.5 = 1.695582496 Reorder the terms: -0.5 + x = 1.695582496 Solving -0.5 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.695582496 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.695582496 + 0.5 x = 1.695582496 + 0.5 Combine like terms: 1.695582496 + 0.5 = 2.195582496 x = 2.195582496 Simplifying x = 2.195582496Subproblem 2
x + -0.5 = -1.695582496 Simplifying x + -0.5 = -1.695582496 Reorder the terms: -0.5 + x = -1.695582496 Solving -0.5 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.695582496 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.695582496 + 0.5 x = -1.695582496 + 0.5 Combine like terms: -1.695582496 + 0.5 = -1.195582496 x = -1.195582496 Simplifying x = -1.195582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.195582496, -1.195582496}Solution
x = {2.195582496, -1.195582496}
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