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Simplifying 10x2 + 20x + -57 = -5 Reorder the terms: -57 + 20x + 10x2 = -5 Solving -57 + 20x + 10x2 = -5 Solving for variable 'x'. Reorder the terms: -57 + 5 + 20x + 10x2 = -5 + 5 Combine like terms: -57 + 5 = -52 -52 + 20x + 10x2 = -5 + 5 Combine like terms: -5 + 5 = 0 -52 + 20x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-26 + 10x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-26 + 10x + 5x2)' equal to zero and attempt to solve: Simplifying -26 + 10x + 5x2 = 0 Solving -26 + 10x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.2 + 2x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + 2x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + 2x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + 2x + x2 = 0 + 5.2 2x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 2x + x2 = 5.2 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 5.2 + 1 Reorder the terms: 1 + 2x + x2 = 5.2 + 1 Combine like terms: 5.2 + 1 = 6.2 1 + 2x + x2 = 6.2 Factor a perfect square on the left side: (x + 1)(x + 1) = 6.2 Calculate the square root of the right side: 2.48997992 Break this problem into two subproblems by setting (x + 1) equal to 2.48997992 and -2.48997992.Subproblem 1
x + 1 = 2.48997992 Simplifying x + 1 = 2.48997992 Reorder the terms: 1 + x = 2.48997992 Solving 1 + x = 2.48997992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.48997992 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.48997992 + -1 x = 2.48997992 + -1 Combine like terms: 2.48997992 + -1 = 1.48997992 x = 1.48997992 Simplifying x = 1.48997992Subproblem 2
x + 1 = -2.48997992 Simplifying x + 1 = -2.48997992 Reorder the terms: 1 + x = -2.48997992 Solving 1 + x = -2.48997992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.48997992 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.48997992 + -1 x = -2.48997992 + -1 Combine like terms: -2.48997992 + -1 = -3.48997992 x = -3.48997992 Simplifying x = -3.48997992Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.48997992, -3.48997992}Solution
x = {1.48997992, -3.48997992}
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