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Simplifying 8x(4x + 3) + -5x = 1 Reorder the terms: 8x(3 + 4x) + -5x = 1 (3 * 8x + 4x * 8x) + -5x = 1 (24x + 32x2) + -5x = 1 Reorder the terms: 24x + -5x + 32x2 = 1 Combine like terms: 24x + -5x = 19x 19x + 32x2 = 1 Solving 19x + 32x2 = 1 Solving for variable 'x'. Reorder the terms: -1 + 19x + 32x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 19x + 32x2 = 0 Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. -0.03125 + 0.59375x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + 0.59375x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + 0.59375x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + 0.59375x + x2 = 0 + 0.03125 0.59375x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 0.59375x + x2 = 0.03125 The x term is 0.59375x. Take half its coefficient (0.296875). Square it (0.08813476563) and add it to both sides. Add '0.08813476563' to each side of the equation. 0.59375x + 0.08813476563 + x2 = 0.03125 + 0.08813476563 Reorder the terms: 0.08813476563 + 0.59375x + x2 = 0.03125 + 0.08813476563 Combine like terms: 0.03125 + 0.08813476563 = 0.11938476563 0.08813476563 + 0.59375x + x2 = 0.11938476563 Factor a perfect square on the left side: (x + 0.296875)(x + 0.296875) = 0.11938476563 Calculate the square root of the right side: 0.345521006 Break this problem into two subproblems by setting (x + 0.296875) equal to 0.345521006 and -0.345521006.Subproblem 1
x + 0.296875 = 0.345521006 Simplifying x + 0.296875 = 0.345521006 Reorder the terms: 0.296875 + x = 0.345521006 Solving 0.296875 + x = 0.345521006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.296875' to each side of the equation. 0.296875 + -0.296875 + x = 0.345521006 + -0.296875 Combine like terms: 0.296875 + -0.296875 = 0.000000 0.000000 + x = 0.345521006 + -0.296875 x = 0.345521006 + -0.296875 Combine like terms: 0.345521006 + -0.296875 = 0.048646006 x = 0.048646006 Simplifying x = 0.048646006Subproblem 2
x + 0.296875 = -0.345521006 Simplifying x + 0.296875 = -0.345521006 Reorder the terms: 0.296875 + x = -0.345521006 Solving 0.296875 + x = -0.345521006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.296875' to each side of the equation. 0.296875 + -0.296875 + x = -0.345521006 + -0.296875 Combine like terms: 0.296875 + -0.296875 = 0.000000 0.000000 + x = -0.345521006 + -0.296875 x = -0.345521006 + -0.296875 Combine like terms: -0.345521006 + -0.296875 = -0.642396006 x = -0.642396006 Simplifying x = -0.642396006Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.048646006, -0.642396006}
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