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Simplifying -16x2 + 48x + 10 = 0 Reorder the terms: 10 + 48x + -16x2 = 0 Solving 10 + 48x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + 24x + -8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + 24x + -8x2)' equal to zero and attempt to solve: Simplifying 5 + 24x + -8x2 = 0 Solving 5 + 24x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.625 + -3x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3x + x2 = 0 + 0.625 -3x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3x + x2 = 0.625 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 0.625 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 0.625 + 2.25 Combine like terms: 0.625 + 2.25 = 2.875 2.25 + -3x + x2 = 2.875 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.875 Calculate the square root of the right side: 1.695582496 Break this problem into two subproblems by setting (x + -1.5) equal to 1.695582496 and -1.695582496.Subproblem 1
x + -1.5 = 1.695582496 Simplifying x + -1.5 = 1.695582496 Reorder the terms: -1.5 + x = 1.695582496 Solving -1.5 + x = 1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.695582496 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.695582496 + 1.5 x = 1.695582496 + 1.5 Combine like terms: 1.695582496 + 1.5 = 3.195582496 x = 3.195582496 Simplifying x = 3.195582496Subproblem 2
x + -1.5 = -1.695582496 Simplifying x + -1.5 = -1.695582496 Reorder the terms: -1.5 + x = -1.695582496 Solving -1.5 + x = -1.695582496 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.695582496 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.695582496 + 1.5 x = -1.695582496 + 1.5 Combine like terms: -1.695582496 + 1.5 = -0.195582496 x = -0.195582496 Simplifying x = -0.195582496Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.195582496, -0.195582496}Solution
x = {3.195582496, -0.195582496}
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