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Simplifying 16x2 + 48x + -14 = 0 Reorder the terms: -14 + 48x + 16x2 = 0 Solving -14 + 48x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 24x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 24x + 8x2)' equal to zero and attempt to solve: Simplifying -7 + 24x + 8x2 = 0 Solving -7 + 24x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.875 + 3x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 3x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 3x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 3x + x2 = 0 + 0.875 3x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 3x + x2 = 0.875 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 = 0.875 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 0.875 + 2.25 Combine like terms: 0.875 + 2.25 = 3.125 2.25 + 3x + x2 = 3.125 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 3.125 Calculate the square root of the right side: 1.767766953 Break this problem into two subproblems by setting (x + 1.5) equal to 1.767766953 and -1.767766953.Subproblem 1
x + 1.5 = 1.767766953 Simplifying x + 1.5 = 1.767766953 Reorder the terms: 1.5 + x = 1.767766953 Solving 1.5 + x = 1.767766953 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 = 1.767766953 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.767766953 + -1.5 x = 1.767766953 + -1.5 Combine like terms: 1.767766953 + -1.5 = 0.267766953 x = 0.267766953 Simplifying x = 0.267766953Subproblem 2
x + 1.5 = -1.767766953 Simplifying x + 1.5 = -1.767766953 Reorder the terms: 1.5 + x = -1.767766953 Solving 1.5 + x = -1.767766953 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 = -1.767766953 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.767766953 + -1.5 x = -1.767766953 + -1.5 Combine like terms: -1.767766953 + -1.5 = -3.267766953 x = -3.267766953 Simplifying x = -3.267766953Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.267766953, -3.267766953}Solution
x = {0.267766953, -3.267766953}
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