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Simplifying 4x2 + 8x + -42 = 0 Reorder the terms: -42 + 8x + 4x2 = 0 Solving -42 + 8x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-21 + 4x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-21 + 4x + 2x2)' equal to zero and attempt to solve: Simplifying -21 + 4x + 2x2 = 0 Solving -21 + 4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -10.5 + 2x + x2 = 0 Move the constant term to the right: Add '10.5' to each side of the equation. -10.5 + 2x + 10.5 + x2 = 0 + 10.5 Reorder the terms: -10.5 + 10.5 + 2x + x2 = 0 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + 2x + x2 = 0 + 10.5 2x + x2 = 0 + 10.5 Combine like terms: 0 + 10.5 = 10.5 2x + x2 = 10.5 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10.5 + 1 Reorder the terms: 1 + 2x + x2 = 10.5 + 1 Combine like terms: 10.5 + 1 = 11.5 1 + 2x + x2 = 11.5 Factor a perfect square on the left side: (x + 1)(x + 1) = 11.5 Calculate the square root of the right side: 3.391164992 Break this problem into two subproblems by setting (x + 1) equal to 3.391164992 and -3.391164992.Subproblem 1
x + 1 = 3.391164992 Simplifying x + 1 = 3.391164992 Reorder the terms: 1 + x = 3.391164992 Solving 1 + x = 3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.391164992 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.391164992 + -1 x = 3.391164992 + -1 Combine like terms: 3.391164992 + -1 = 2.391164992 x = 2.391164992 Simplifying x = 2.391164992Subproblem 2
x + 1 = -3.391164992 Simplifying x + 1 = -3.391164992 Reorder the terms: 1 + x = -3.391164992 Solving 1 + x = -3.391164992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.391164992 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.391164992 + -1 x = -3.391164992 + -1 Combine like terms: -3.391164992 + -1 = -4.391164992 x = -4.391164992 Simplifying x = -4.391164992Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.391164992, -4.391164992}Solution
x = {2.391164992, -4.391164992}
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