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Simplifying 432x2 + 2x + -2 = 0 Reorder the terms: -2 + 2x + 432x2 = 0 Solving -2 + 2x + 432x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + x + 216x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + x + 216x2)' equal to zero and attempt to solve: Simplifying -1 + x + 216x2 = 0 Solving -1 + x + 216x2 = 0 Begin completing the square. Divide all terms by 216 the coefficient of the squared term: Divide each side by '216'. -0.00462962963 + 0.004629629630x + x2 = 0 Move the constant term to the right: Add '0.00462962963' to each side of the equation. -0.00462962963 + 0.004629629630x + 0.00462962963 + x2 = 0 + 0.00462962963 Reorder the terms: -0.00462962963 + 0.00462962963 + 0.004629629630x + x2 = 0 + 0.00462962963 Combine like terms: -0.00462962963 + 0.00462962963 = 0.00000000000 0.00000000000 + 0.004629629630x + x2 = 0 + 0.00462962963 0.004629629630x + x2 = 0 + 0.00462962963 Combine like terms: 0 + 0.00462962963 = 0.00462962963 0.004629629630x + x2 = 0.00462962963 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. 0.004629629630x + 0.25 + x2 = 0.00462962963 + 0.25 Reorder the terms: 0.25 + 0.004629629630x + x2 = 0.00462962963 + 0.25 Combine like terms: 0.00462962963 + 0.25 = 0.25462962963 0.25 + 0.004629629630x + x2 = 0.25462962963 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.25462962963 Calculate the square root of the right side: 0.504608392 Break this problem into two subproblems by setting (x + 0.5) equal to 0.504608392 and -0.504608392.Subproblem 1
x + 0.5 = 0.504608392 Simplifying x + 0.5 = 0.504608392 Reorder the terms: 0.5 + x = 0.504608392 Solving 0.5 + x = 0.504608392 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 = 0.504608392 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.504608392 + -0.5 x = 0.504608392 + -0.5 Combine like terms: 0.504608392 + -0.5 = 0.004608392 x = 0.004608392 Simplifying x = 0.004608392Subproblem 2
x + 0.5 = -0.504608392 Simplifying x + 0.5 = -0.504608392 Reorder the terms: 0.5 + x = -0.504608392 Solving 0.5 + x = -0.504608392 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 = -0.504608392 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.504608392 + -0.5 x = -0.504608392 + -0.5 Combine like terms: -0.504608392 + -0.5 = -1.004608392 x = -1.004608392 Simplifying x = -1.004608392Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.004608392, -1.004608392}Solution
x = {0.004608392, -1.004608392}
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