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Simplifying x(16x2 + 16x + -18) = 0 Reorder the terms: x(-18 + 16x + 16x2) = 0 (-18 * x + 16x * x + 16x2 * x) = 0 (-18x + 16x2 + 16x3) = 0 Solving -18x + 16x2 + 16x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-9 + 8x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-9 + 8x + 8x2)' equal to zero and attempt to solve: Simplifying -9 + 8x + 8x2 = 0 Solving -9 + 8x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + x + x2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + x + 1.125 + x2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + x + x2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x + x2 = 0 + 1.125 x + x2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 x + x2 = 1.125 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. + 0.25 + x2 = 1.125 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 1.125 + 0.25 Combine like terms: 1.125 + 0.25 = 1.375 1.25 + x2 = 1.375 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 1.375 Calculate the square root of the right side: 1.17260394 Break this problem into two subproblems by setting (x + 0.5) equal to 1.17260394 and -1.17260394.Subproblem 1
x + 0.5 = 1.17260394 Simplifying x + 0.5 = 1.17260394 Reorder the terms: 0.5 + x = 1.17260394 Solving 0.5 + x = 1.17260394 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 = 1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.17260394 + -0.5 x = 1.17260394 + -0.5 Combine like terms: 1.17260394 + -0.5 = 0.67260394 x = 0.67260394 Simplifying x = 0.67260394Subproblem 2
x + 0.5 = -1.17260394 Simplifying x + 0.5 = -1.17260394 Reorder the terms: 0.5 + x = -1.17260394 Solving 0.5 + x = -1.17260394 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 = -1.17260394 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.17260394 + -0.5 x = -1.17260394 + -0.5 Combine like terms: -1.17260394 + -0.5 = -1.67260394 x = -1.67260394 Simplifying x = -1.67260394Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.67260394, -1.67260394}Solution
x = {0, 0.67260394, -1.67260394}
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