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Simplifying 20x2 + -48x + 14 = 0 Reorder the terms: 14 + -48x + 20x2 = 0 Solving 14 + -48x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(7 + -24x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(7 + -24x + 10x2)' equal to zero and attempt to solve: Simplifying 7 + -24x + 10x2 = 0 Solving 7 + -24x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. 0.7 + -2.4x + x2 = 0.0 Move the constant term to the right: Add '-0.7' to each side of the equation. 0.7 + -2.4x + -0.7 + x2 = 0.0 + -0.7 Reorder the terms: 0.7 + -0.7 + -2.4x + x2 = 0.0 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + -2.4x + x2 = 0.0 + -0.7 -2.4x + x2 = 0.0 + -0.7 Combine like terms: 0.0 + -0.7 = -0.7 -2.4x + x2 = -0.7 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.7 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.7 + 1.44 Combine like terms: -0.7 + 1.44 = 0.74 1.44 + -2.4x + x2 = 0.74 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.74 Calculate the square root of the right side: 0.860232527 Break this problem into two subproblems by setting (x + -1.2) equal to 0.860232527 and -0.860232527.Subproblem 1
x + -1.2 = 0.860232527 Simplifying x + -1.2 = 0.860232527 Reorder the terms: -1.2 + x = 0.860232527 Solving -1.2 + x = 0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.860232527 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.860232527 + 1.2 x = 0.860232527 + 1.2 Combine like terms: 0.860232527 + 1.2 = 2.060232527 x = 2.060232527 Simplifying x = 2.060232527Subproblem 2
x + -1.2 = -0.860232527 Simplifying x + -1.2 = -0.860232527 Reorder the terms: -1.2 + x = -0.860232527 Solving -1.2 + x = -0.860232527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.860232527 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.860232527 + 1.2 x = -0.860232527 + 1.2 Combine like terms: -0.860232527 + 1.2 = 0.339767473 x = 0.339767473 Simplifying x = 0.339767473Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.060232527, 0.339767473}Solution
x = {2.060232527, 0.339767473}
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