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Simplifying 10x2 + 14x + -44 = 0 Reorder the terms: -44 + 14x + 10x2 = 0 Solving -44 + 14x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 7x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying -22 + 7x + 5x2 = 0 Solving -22 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4.4 + 1.4x + x2 = 0 Move the constant term to the right: Add '4.4' to each side of the equation. -4.4 + 1.4x + 4.4 + x2 = 0 + 4.4 Reorder the terms: -4.4 + 4.4 + 1.4x + x2 = 0 + 4.4 Combine like terms: -4.4 + 4.4 = 0.0 0.0 + 1.4x + x2 = 0 + 4.4 1.4x + x2 = 0 + 4.4 Combine like terms: 0 + 4.4 = 4.4 1.4x + x2 = 4.4 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = 4.4 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = 4.4 + 0.49 Combine like terms: 4.4 + 0.49 = 4.89 0.49 + 1.4x + x2 = 4.89 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = 4.89 Calculate the square root of the right side: 2.211334439 Break this problem into two subproblems by setting (x + 0.7) equal to 2.211334439 and -2.211334439.Subproblem 1
x + 0.7 = 2.211334439 Simplifying x + 0.7 = 2.211334439 Reorder the terms: 0.7 + x = 2.211334439 Solving 0.7 + x = 2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = 2.211334439 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = 2.211334439 + -0.7 x = 2.211334439 + -0.7 Combine like terms: 2.211334439 + -0.7 = 1.511334439 x = 1.511334439 Simplifying x = 1.511334439Subproblem 2
x + 0.7 = -2.211334439 Simplifying x + 0.7 = -2.211334439 Reorder the terms: 0.7 + x = -2.211334439 Solving 0.7 + x = -2.211334439 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + x = -2.211334439 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + x = -2.211334439 + -0.7 x = -2.211334439 + -0.7 Combine like terms: -2.211334439 + -0.7 = -2.911334439 x = -2.911334439 Simplifying x = -2.911334439Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.511334439, -2.911334439}Solution
x = {1.511334439, -2.911334439}
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