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Simplifying 16x2 + 16x + -28 = 0 Reorder the terms: -28 + 16x + 16x2 = 0 Solving -28 + 16x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-7 + 4x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + 4x + 4x2)' equal to zero and attempt to solve: Simplifying -7 + 4x + 4x2 = 0 Solving -7 + 4x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x + x2 = 0 + 1.75 x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 x + x2 = 1.75 The x term is x. 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. + 0.25 + x2 = 1.75 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.75 + 0.25 Combine like terms: 1.75 + 0.25 = 2 1.25 + x2 = 2 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (x + 0.5) equal to 1.414213562 and -1.414213562.Subproblem 1
x + 0.5 = 1.414213562 Simplifying x + 0.5 = 1.414213562 Reorder the terms: 0.5 + x = 1.414213562 Solving 0.5 + x = 1.414213562 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 = 1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.414213562 + -0.5 x = 1.414213562 + -0.5 Combine like terms: 1.414213562 + -0.5 = 0.914213562 x = 0.914213562 Simplifying x = 0.914213562Subproblem 2
x + 0.5 = -1.414213562 Simplifying x + 0.5 = -1.414213562 Reorder the terms: 0.5 + x = -1.414213562 Solving 0.5 + x = -1.414213562 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 = -1.414213562 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.414213562 + -0.5 x = -1.414213562 + -0.5 Combine like terms: -1.414213562 + -0.5 = -1.914213562 x = -1.914213562 Simplifying x = -1.914213562Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.914213562, -1.914213562}Solution
x = {0.914213562, -1.914213562}
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