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Simplifying (x + -19 + 8x2)(2) = 0 Reorder the terms: (-19 + x + 8x2)(2) = 0 Reorder the terms for easier multiplication: 2(-19 + x + 8x2) = 0 (-19 * 2 + x * 2 + 8x2 * 2) = 0 (-38 + 2x + 16x2) = 0 Solving -38 + 2x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-19 + x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-19 + x + 8x2)' equal to zero and attempt to solve: Simplifying -19 + x + 8x2 = 0 Solving -19 + x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -2.375 + 0.125x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + 0.125x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + 0.125x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + 0.125x + x2 = 0 + 2.375 0.125x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 0.125x + x2 = 2.375 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.125x + 0.25 + x2 = 2.375 + 0.25 Reorder the terms: 0.25 + 0.125x + x2 = 2.375 + 0.25 Combine like terms: 2.375 + 0.25 = 2.625 0.25 + 0.125x + x2 = 2.625 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 2.625 Calculate the square root of the right side: 1.620185175 Break this problem into two subproblems by setting (x + 0.5) equal to 1.620185175 and -1.620185175.Subproblem 1
x + 0.5 = 1.620185175 Simplifying x + 0.5 = 1.620185175 Reorder the terms: 0.5 + x = 1.620185175 Solving 0.5 + x = 1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.620185175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.620185175 + -0.5 x = 1.620185175 + -0.5 Combine like terms: 1.620185175 + -0.5 = 1.120185175 x = 1.120185175 Simplifying x = 1.120185175Subproblem 2
x + 0.5 = -1.620185175 Simplifying x + 0.5 = -1.620185175 Reorder the terms: 0.5 + x = -1.620185175 Solving 0.5 + x = -1.620185175 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.620185175 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.620185175 + -0.5 x = -1.620185175 + -0.5 Combine like terms: -1.620185175 + -0.5 = -2.120185175 x = -2.120185175 Simplifying x = -2.120185175Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.120185175, -2.120185175}Solution
x = {1.120185175, -2.120185175}
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