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Simplifying 20x2 + -4x + -48 = 0 Reorder the terms: -48 + -4x + 20x2 = 0 Solving -48 + -4x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-12 + -1x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-12 + -1x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + -1x + 5x2 = 0 Solving -12 + -1x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -0.2x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -0.2x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -0.2x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -0.2x + x2 = 0 + 2.4 -0.2x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -0.2x + x2 = 2.4 The x term is -0.2x. Take half its coefficient (-0.1). Square it (0.01) and add it to both sides. Add '0.01' to each side of the equation. -0.2x + 0.01 + x2 = 2.4 + 0.01 Reorder the terms: 0.01 + -0.2x + x2 = 2.4 + 0.01 Combine like terms: 2.4 + 0.01 = 2.41 0.01 + -0.2x + x2 = 2.41 Factor a perfect square on the left side: (x + -0.1)(x + -0.1) = 2.41 Calculate the square root of the right side: 1.55241747 Break this problem into two subproblems by setting (x + -0.1) equal to 1.55241747 and -1.55241747.Subproblem 1
x + -0.1 = 1.55241747 Simplifying x + -0.1 = 1.55241747 Reorder the terms: -0.1 + x = 1.55241747 Solving -0.1 + x = 1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 1.55241747 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 1.55241747 + 0.1 x = 1.55241747 + 0.1 Combine like terms: 1.55241747 + 0.1 = 1.65241747 x = 1.65241747 Simplifying x = 1.65241747Subproblem 2
x + -0.1 = -1.55241747 Simplifying x + -0.1 = -1.55241747 Reorder the terms: -0.1 + x = -1.55241747 Solving -0.1 + x = -1.55241747 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = -1.55241747 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = -1.55241747 + 0.1 x = -1.55241747 + 0.1 Combine like terms: -1.55241747 + 0.1 = -1.45241747 x = -1.45241747 Simplifying x = -1.45241747Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.65241747, -1.45241747}Solution
x = {1.65241747, -1.45241747}
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