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Simplifying 15 = -16x2 + 52x + 25 Reorder the terms: 15 = 25 + 52x + -16x2 Solving 15 = 25 + 52x + -16x2 Solving for variable 'x'. Combine like terms: 15 + -25 = -10 -10 + -52x + 16x2 = 25 + 52x + -16x2 + -25 + -52x + 16x2 Reorder the terms: -10 + -52x + 16x2 = 25 + -25 + 52x + -52x + -16x2 + 16x2 Combine like terms: 25 + -25 = 0 -10 + -52x + 16x2 = 0 + 52x + -52x + -16x2 + 16x2 -10 + -52x + 16x2 = 52x + -52x + -16x2 + 16x2 Combine like terms: 52x + -52x = 0 -10 + -52x + 16x2 = 0 + -16x2 + 16x2 -10 + -52x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -10 + -52x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -26x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -26x + 8x2)' equal to zero and attempt to solve: Simplifying -5 + -26x + 8x2 = 0 Solving -5 + -26x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -3.25x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3.25x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3.25x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3.25x + x2 = 0 + 0.625 -3.25x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3.25x + x2 = 0.625 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 = 0.625 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 0.625 + 2.640625 Combine like terms: 0.625 + 2.640625 = 3.265625 2.640625 + -3.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + -1.625) equal to 1.807104037 and -1.807104037.Subproblem 1
x + -1.625 = 1.807104037 Simplifying x + -1.625 = 1.807104037 Reorder the terms: -1.625 + x = 1.807104037 Solving -1.625 + x = 1.807104037 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 = 1.807104037 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.807104037 + 1.625 x = 1.807104037 + 1.625 Combine like terms: 1.807104037 + 1.625 = 3.432104037 x = 3.432104037 Simplifying x = 3.432104037Subproblem 2
x + -1.625 = -1.807104037 Simplifying x + -1.625 = -1.807104037 Reorder the terms: -1.625 + x = -1.807104037 Solving -1.625 + x = -1.807104037 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 = -1.807104037 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.807104037 + 1.625 x = -1.807104037 + 1.625 Combine like terms: -1.807104037 + 1.625 = -0.182104037 x = -0.182104037 Simplifying x = -0.182104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.432104037, -0.182104037}Solution
x = {3.432104037, -0.182104037}
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