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Simplifying 10x2 + -82x + 10 = 0 Reorder the terms: 10 + -82x + 10x2 = 0 Solving 10 + -82x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -41x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -41x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + -41x + 5x2 = 0 Solving 5 + -41x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -8.2x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -8.2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -8.2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8.2x + x2 = 0 + -1 -8.2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8.2x + x2 = -1 The x term is -8.2x. Take half its coefficient (-4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. -8.2x + 16.81 + x2 = -1 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = -1 + 16.81 Combine like terms: -1 + 16.81 = 15.81 16.81 + -8.2x + x2 = 15.81 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 15.81 Calculate the square root of the right side: 3.97617907 Break this problem into two subproblems by setting (x + -4.1) equal to 3.97617907 and -3.97617907.Subproblem 1
x + -4.1 = 3.97617907 Simplifying x + -4.1 = 3.97617907 Reorder the terms: -4.1 + x = 3.97617907 Solving -4.1 + x = 3.97617907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = 3.97617907 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 3.97617907 + 4.1 x = 3.97617907 + 4.1 Combine like terms: 3.97617907 + 4.1 = 8.07617907 x = 8.07617907 Simplifying x = 8.07617907Subproblem 2
x + -4.1 = -3.97617907 Simplifying x + -4.1 = -3.97617907 Reorder the terms: -4.1 + x = -3.97617907 Solving -4.1 + x = -3.97617907 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.1' to each side of the equation. -4.1 + 4.1 + x = -3.97617907 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -3.97617907 + 4.1 x = -3.97617907 + 4.1 Combine like terms: -3.97617907 + 4.1 = 0.12382093 x = 0.12382093 Simplifying x = 0.12382093Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.07617907, 0.12382093}Solution
x = {8.07617907, 0.12382093}
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