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Simplifying 8x2 + -32x + 13 = 0 Reorder the terms: 13 + -32x + 8x2 = 0 Solving 13 + -32x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.625 + -4x + x2 = 0 Move the constant term to the right: Add '-1.625' to each side of the equation. 1.625 + -4x + -1.625 + x2 = 0 + -1.625 Reorder the terms: 1.625 + -1.625 + -4x + x2 = 0 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + -4x + x2 = 0 + -1.625 -4x + x2 = 0 + -1.625 Combine like terms: 0 + -1.625 = -1.625 -4x + x2 = -1.625 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -1.625 + 4 Reorder the terms: 4 + -4x + x2 = -1.625 + 4 Combine like terms: -1.625 + 4 = 2.375 4 + -4x + x2 = 2.375 Factor a perfect square on the left side: (x + -2)(x + -2) = 2.375 Calculate the square root of the right side: 1.541103501 Break this problem into two subproblems by setting (x + -2) equal to 1.541103501 and -1.541103501.Subproblem 1
x + -2 = 1.541103501 Simplifying x + -2 = 1.541103501 Reorder the terms: -2 + x = 1.541103501 Solving -2 + x = 1.541103501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.541103501 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.541103501 + 2 x = 1.541103501 + 2 Combine like terms: 1.541103501 + 2 = 3.541103501 x = 3.541103501 Simplifying x = 3.541103501Subproblem 2
x + -2 = -1.541103501 Simplifying x + -2 = -1.541103501 Reorder the terms: -2 + x = -1.541103501 Solving -2 + x = -1.541103501 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.541103501 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.541103501 + 2 x = -1.541103501 + 2 Combine like terms: -1.541103501 + 2 = 0.458896499 x = 0.458896499 Simplifying x = 0.458896499Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.541103501, 0.458896499}
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