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Simplifying 20x2 + 4x + -6 = 0 Reorder the terms: -6 + 4x + 20x2 = 0 Solving -6 + 4x + 20x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + 2x + 10x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + 2x + 10x2)' equal to zero and attempt to solve: Simplifying -3 + 2x + 10x2 = 0 Solving -3 + 2x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.3 + 0.2x + x2 = 0.0 Move the constant term to the right: Add '0.3' to each side of the equation. -0.3 + 0.2x + 0.3 + x2 = 0.0 + 0.3 Reorder the terms: -0.3 + 0.3 + 0.2x + x2 = 0.0 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + 0.2x + x2 = 0.0 + 0.3 0.2x + x2 = 0.0 + 0.3 Combine like terms: 0.0 + 0.3 = 0.3 0.2x + x2 = 0.3 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 = 0.3 + 0.01 Reorder the terms: 0.01 + 0.2x + x2 = 0.3 + 0.01 Combine like terms: 0.3 + 0.01 = 0.31 0.01 + 0.2x + x2 = 0.31 Factor a perfect square on the left side: (x + 0.1)(x + 0.1) = 0.31 Calculate the square root of the right side: 0.556776436 Break this problem into two subproblems by setting (x + 0.1) equal to 0.556776436 and -0.556776436.Subproblem 1
x + 0.1 = 0.556776436 Simplifying x + 0.1 = 0.556776436 Reorder the terms: 0.1 + x = 0.556776436 Solving 0.1 + x = 0.556776436 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 = 0.556776436 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = 0.556776436 + -0.1 x = 0.556776436 + -0.1 Combine like terms: 0.556776436 + -0.1 = 0.456776436 x = 0.456776436 Simplifying x = 0.456776436Subproblem 2
x + 0.1 = -0.556776436 Simplifying x + 0.1 = -0.556776436 Reorder the terms: 0.1 + x = -0.556776436 Solving 0.1 + x = -0.556776436 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 = -0.556776436 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + x = -0.556776436 + -0.1 x = -0.556776436 + -0.1 Combine like terms: -0.556776436 + -0.1 = -0.656776436 x = -0.656776436 Simplifying x = -0.656776436Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.456776436, -0.656776436}Solution
x = {0.456776436, -0.656776436}
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