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Simplifying 4x(2x + 8) + -1 = 5 Reorder the terms: 4x(8 + 2x) + -1 = 5 (8 * 4x + 2x * 4x) + -1 = 5 (32x + 8x2) + -1 = 5 Reorder the terms: -1 + 32x + 8x2 = 5 Solving -1 + 32x + 8x2 = 5 Solving for variable 'x'. Reorder the terms: -1 + -5 + 32x + 8x2 = 5 + -5 Combine like terms: -1 + -5 = -6 -6 + 32x + 8x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -6 + 32x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 16x + 4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 16x + 4x2)' equal to zero and attempt to solve: Simplifying -3 + 16x + 4x2 = 0 Solving -3 + 16x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.75 + 4x + x2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + 4x + 0.75 + x2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + 4x + x2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + 4x + x2 = 0 + 0.75 4x + x2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 4x + x2 = 0.75 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 = 0.75 + 4 Reorder the terms: 4 + 4x + x2 = 0.75 + 4 Combine like terms: 0.75 + 4 = 4.75 4 + 4x + x2 = 4.75 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 2) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 2 = 2.179449472 Simplifying x + 2 = 2.179449472 Reorder the terms: 2 + x = 2.179449472 Solving 2 + x = 2.179449472 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 = 2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.179449472 + -2 x = 2.179449472 + -2 Combine like terms: 2.179449472 + -2 = 0.179449472 x = 0.179449472 Simplifying x = 0.179449472Subproblem 2
x + 2 = -2.179449472 Simplifying x + 2 = -2.179449472 Reorder the terms: 2 + x = -2.179449472 Solving 2 + x = -2.179449472 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 = -2.179449472 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.179449472 + -2 x = -2.179449472 + -2 Combine like terms: -2.179449472 + -2 = -4.179449472 x = -4.179449472 Simplifying x = -4.179449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.179449472, -4.179449472}Solution
x = {0.179449472, -4.179449472}
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