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Simplifying 5x2 + -16x + 10 = 0 Reorder the terms: 10 + -16x + 5x2 = 0 Solving 10 + -16x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + -3.2x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -3.2x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -3.2x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3.2x + x2 = 0 + -2 -3.2x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -3.2x + x2 = -2 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 = -2 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = -2 + 2.56 Combine like terms: -2 + 2.56 = 0.56 2.56 + -3.2x + x2 = 0.56 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x + -1.6) equal to 0.748331477 and -0.748331477.Subproblem 1
x + -1.6 = 0.748331477 Simplifying x + -1.6 = 0.748331477 Reorder the terms: -1.6 + x = 0.748331477 Solving -1.6 + x = 0.748331477 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 = 0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 0.748331477 + 1.6 x = 0.748331477 + 1.6 Combine like terms: 0.748331477 + 1.6 = 2.348331477 x = 2.348331477 Simplifying x = 2.348331477Subproblem 2
x + -1.6 = -0.748331477 Simplifying x + -1.6 = -0.748331477 Reorder the terms: -1.6 + x = -0.748331477 Solving -1.6 + x = -0.748331477 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 = -0.748331477 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -0.748331477 + 1.6 x = -0.748331477 + 1.6 Combine like terms: -0.748331477 + 1.6 = 0.851668523 x = 0.851668523 Simplifying x = 0.851668523Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.348331477, 0.851668523}
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