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Simplifying 10x2 + 4x + -24 = 0 Reorder the terms: -24 + 4x + 10x2 = 0 Solving -24 + 4x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + 2x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + 2x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + 2x + 5x2 = 0 Solving -12 + 2x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + 0.4x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + 0.4x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + 0.4x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + 0.4x + x2 = 0 + 2.4 0.4x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 0.4x + x2 = 2.4 The x term is 0.4x. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4x + 0.04 + x2 = 2.4 + 0.04 Reorder the terms: 0.04 + 0.4x + x2 = 2.4 + 0.04 Combine like terms: 2.4 + 0.04 = 2.44 0.04 + 0.4x + x2 = 2.44 Factor a perfect square on the left side: (x + 0.2)(x + 0.2) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x + 0.2) equal to 1.562049935 and -1.562049935.Subproblem 1
x + 0.2 = 1.562049935 Simplifying x + 0.2 = 1.562049935 Reorder the terms: 0.2 + x = 1.562049935 Solving 0.2 + x = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.562049935 + -0.2 x = 1.562049935 + -0.2 Combine like terms: 1.562049935 + -0.2 = 1.362049935 x = 1.362049935 Simplifying x = 1.362049935Subproblem 2
x + 0.2 = -1.562049935 Simplifying x + 0.2 = -1.562049935 Reorder the terms: 0.2 + x = -1.562049935 Solving 0.2 + x = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.562049935 + -0.2 x = -1.562049935 + -0.2 Combine like terms: -1.562049935 + -0.2 = -1.762049935 x = -1.762049935 Simplifying x = -1.762049935Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.362049935, -1.762049935}Solution
x = {1.362049935, -1.762049935}
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