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Simplifying 16x2 + 52x + -26 = 0 Reorder the terms: -26 + 52x + 16x2 = 0 Solving -26 + 52x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 26x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 26x + 8x2)' equal to zero and attempt to solve: Simplifying -13 + 26x + 8x2 = 0 Solving -13 + 26x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.625 + 3.25x + x2 = 0 Move the constant term to the right: Add '1.625' to each side of the equation. -1.625 + 3.25x + 1.625 + x2 = 0 + 1.625 Reorder the terms: -1.625 + 1.625 + 3.25x + x2 = 0 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + 3.25x + x2 = 0 + 1.625 3.25x + x2 = 0 + 1.625 Combine like terms: 0 + 1.625 = 1.625 3.25x + x2 = 1.625 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 = 1.625 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 1.625 + 2.640625 Combine like terms: 1.625 + 2.640625 = 4.265625 2.640625 + 3.25x + x2 = 4.265625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 4.265625 Calculate the square root of the right side: 2.065338955 Break this problem into two subproblems by setting (x + 1.625) equal to 2.065338955 and -2.065338955.Subproblem 1
x + 1.625 = 2.065338955 Simplifying x + 1.625 = 2.065338955 Reorder the terms: 1.625 + x = 2.065338955 Solving 1.625 + x = 2.065338955 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 = 2.065338955 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 2.065338955 + -1.625 x = 2.065338955 + -1.625 Combine like terms: 2.065338955 + -1.625 = 0.440338955 x = 0.440338955 Simplifying x = 0.440338955Subproblem 2
x + 1.625 = -2.065338955 Simplifying x + 1.625 = -2.065338955 Reorder the terms: 1.625 + x = -2.065338955 Solving 1.625 + x = -2.065338955 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 = -2.065338955 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -2.065338955 + -1.625 x = -2.065338955 + -1.625 Combine like terms: -2.065338955 + -1.625 = -3.690338955 x = -3.690338955 Simplifying x = -3.690338955Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.440338955, -3.690338955}Solution
x = {0.440338955, -3.690338955}
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