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Simplifying -16x2 + 52x + 16 = 0 Reorder the terms: 16 + 52x + -16x2 = 0 Solving 16 + 52x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(4 + 13x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(4 + 13x + -4x2)' equal to zero and attempt to solve: Simplifying 4 + 13x + -4x2 = 0 Solving 4 + 13x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -1 + -3.25x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.25x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.25x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.25x + x2 = 0 + 1 -3.25x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.25x + x2 = 1 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 1 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 1 + 2.640625 Combine like terms: 1 + 2.640625 = 3.640625 2.640625 + -3.25x + x2 = 3.640625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 3.640625 Calculate the square root of the right side: 1.90804219 Break this problem into two subproblems by setting (x + -1.625) equal to 1.90804219 and -1.90804219.Subproblem 1
x + -1.625 = 1.90804219 Simplifying x + -1.625 = 1.90804219 Reorder the terms: -1.625 + x = 1.90804219 Solving -1.625 + x = 1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.90804219 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.90804219 + 1.625 x = 1.90804219 + 1.625 Combine like terms: 1.90804219 + 1.625 = 3.53304219 x = 3.53304219 Simplifying x = 3.53304219Subproblem 2
x + -1.625 = -1.90804219 Simplifying x + -1.625 = -1.90804219 Reorder the terms: -1.625 + x = -1.90804219 Solving -1.625 + x = -1.90804219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.90804219 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.90804219 + 1.625 x = -1.90804219 + 1.625 Combine like terms: -1.90804219 + 1.625 = -0.28304219 x = -0.28304219 Simplifying x = -0.28304219Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.53304219, -0.28304219}Solution
x = {3.53304219, -0.28304219}
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