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Simplifying 5x2 + 2 = 16x Reorder the terms: 2 + 5x2 = 16x Solving 2 + 5x2 = 16x Solving for variable 'x'. Reorder the terms: 2 + -16x + 5x2 = 16x + -16x Combine like terms: 16x + -16x = 0 2 + -16x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -3.2x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -3.2x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -3.2x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -3.2x + x2 = 0 + -0.4 -3.2x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -3.2x + x2 = -0.4 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = -0.4 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -0.4 + 2.56 Combine like terms: -0.4 + 2.56 = 2.16 2.56 + -3.2x + x2 = 2.16 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 2.16 Calculate the square root of the right side: 1.469693846 Break this problem into two subproblems by setting (x + -1.6) equal to 1.469693846 and -1.469693846.Subproblem 1
x + -1.6 = 1.469693846 Simplifying x + -1.6 = 1.469693846 Reorder the terms: -1.6 + x = 1.469693846 Solving -1.6 + x = 1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 1.469693846 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 1.469693846 + 1.6 x = 1.469693846 + 1.6 Combine like terms: 1.469693846 + 1.6 = 3.069693846 x = 3.069693846 Simplifying x = 3.069693846Subproblem 2
x + -1.6 = -1.469693846 Simplifying x + -1.6 = -1.469693846 Reorder the terms: -1.6 + x = -1.469693846 Solving -1.6 + x = -1.469693846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -1.469693846 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -1.469693846 + 1.6 x = -1.469693846 + 1.6 Combine like terms: -1.469693846 + 1.6 = 0.130306154 x = 0.130306154 Simplifying x = 0.130306154Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.069693846, 0.130306154}
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